The DOI matches its Crossref record; 236 of the 236 references it cites were found in a registry or an index; none of the 245 sources its claims cite is checked for support yet.
Diffusion Models: A Comprehensive Survey of Methods and Applications
Open accessAbstract
Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language processing, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
This survey organizes diffusion-model research into three core areas—efficient sampling, improved likelihood estimation, and handling data with special structures—and reviews connections to other generative models plus six application domains. It also introduces DDPMs, score-based generative models, and Score SDEs as the main formulations and outlines future research directions.
Key findings
- The paper proposes a taxonomy of diffusion-model advances: efficient sampling, improved likelihood estimation, and methods for data with special structures such as discrete data, invariant structures, and manifold structures.
- Efficient sampling methods are split into learning-free and learning-based approaches; customized ODE solvers such as DPM-solver and exponential integrators can produce high-quality samples in just 10 to 20 iterations, far fewer than the hundreds typically required without accelerated sampling.
- Improved-likelihood methods include noise schedule optimization, reverse variance learning, and exact likelihood computation; Variational Diffusion Models show that noise schedules do not affect the VLB as long as they share the same values at \(R_{\min}\) and \(R_{\max}\), and only affect Monte Carlo estimator variance.
- Applications are grouped into six categories: computer vision, natural language processing, temporal data modeling, multi-modal learning, robust learning, and interdisciplinary applications.
Methods
- Design: a comprehensive survey/overview of diffusion models, not an empirical study with new experiments.
- Data/sample: existing published research literature on diffusion models and related generative models, cited throughout the reference list.
- Main analysis: conceptual and taxonomic synthesis, including a self-contained introduction to DDPMs, SGMs, and Score SDEs, followed by categorized review of methods, connections, applications, and future directions.
Limitations
- Stated: the paper identifies open issues including revisiting assumptions such as complete information erasure in finite time, lack of theoretical understanding for why and when diffusion models work, weaker latent representations than VAEs/GANs, and pitfalls such as dataset bias, improper image generation, and privacy issues.
- Stated: for scene-graph-to-image generation, high-quality paired SG-image datasets are scarce, and leveraging large-scale text-image datasets for augmentation or semantic diffusion priors remains an open problem.
- Evident: the survey does not report a systematic search protocol, inclusion/exclusion criteria, or quantitative meta-analysis, so its coverage is broad but potentially selective.
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In the paper
“They have broken the long-time dominance of generative adversarial networks (GANs) [71] in the challenging task of image synthesis [54,87,223,228]”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
What the sources say
- Not checked yetcites [71]
- Not checked yetcites [54]
- Not checked yetcites [87]
- Not checked yetcites [223]
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Diffusion models [87,218,223,228] have emerged as the new state-of-the-art family of deep generative models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
What the sources say
- Not checked yetcites [87]
- Not checked yetcites [218]
- Not checked yetcites [223]
- Not checked yetcites [228]
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Key to the success of this sampling process is training the reverse Markov chain to match the actual time reversal of the forward Markov chain.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.1 Denoising Diffusion Probabilistic Models (DDPMs)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Numerous methods have been developed to improve diffusion models, either by enhancing empirical performance [165,220,224] or by extending the model capacity from a theoretical perspective [144,145,222,228,279].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
What the sources say
- Not checked yetcites [165]
- Not checked yetcites [220]
- Not checked yetcites [224]
- Not checked yetcites [144]
- Not checked yetcites [145]
- Not checked yetcites [222]
- Not checked yetcites [228]
- Not checked yetcites [279]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Key to all these approaches is to progressively perturb data with intensifying random noise (called the “diffusion” process), then successively remove noise to generate new data samples.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Comparing Equation (14) with Equation (10), it is clear that the training objectives of DDPMs and SGMs are equivalent, once we set ϵ θ (x, t ) = -σ t s θ (x, t ).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.2 Score-Based Generative Models (SGMs)
Strength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“As observed by Sohl-Dickstein et al. (2015) [218], this Gaussian transition kernel allows us to marginalize the joint distribution in Equation (1) to obtain the analytical form of q(x t | x 0 ) for all t ∈ {0, 1, • • • ,T }.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.1 Denoising Diffusion Probabilistic Models (DDPMs)
What the sources say
- Not checked yetcites [218]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When ᾱT ≈ 0, x T is almost Gaussian in distribution, so we have q(”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.1 Denoising Diffusion Probabilistic Models (DDPMs)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“Song et al. (2020) [228] prove that the reverse diffusion method is a numerical SDE solver for the reverse-time SDE in Equation (18).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since the cost of sampling increases proportionally with the number of discretized time steps, many researchers have focused on developing discretization schemes that reduce the number of time steps while also minimizing discretization errors.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1 Learning-Free Sampling
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIn the paper
“Song et al. (2020) [228] show that the reverse Markov chain defined by Equation (5) amounts to a numerical SDE solver for Equation (21).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The solution trajectories of this reverse SDE share the same marginal densities as those of the forward SDE, except that they evolve in the opposite time direction [228].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
What the sources say
- Not checked yetcites [228]
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“The generation process of DDPM [87,218] can be viewed as a particular discretization of the reverse-time SDE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [87]
- Not checked yetcites [218]
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Many samplers for diffusion models rely on discretizing either the reverse-time SDE present in Equation (18) or the probability flow ODE from Equation (19).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1 Learning-Free Sampling
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Crucially, for any diffusion process in the form of Equation (15), Anderson [4] shows that it can be reversed by solving the following reverse-time SDE:”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
What the sources say
- Not checked yetcites [4] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“DDPMs and SGMs can be further generalized to the case of infinite time steps or noise levels, where the perturbation and denoising processes are solutions to stochastic differential equations (SDEs).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Moreover, Song et al. (2020) [228] prove the existence of an ordinary differential equation (ODE), namely the probability flow ODE, whose trajectories have the same marginals as the reversetime SDE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The theory of Langevin Monte Carlo [175] guarantees that as s t → 0 and N → ∞, x (N ) 0 becomes a valid sample from the data distribution q(x 0 ).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.2 Score-Based Generative Models (SGMs)
What the sources say
- Not checked yetcites [175] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Through extensive experimental investigations, Karras et al. (2022) [111] show that Heun's 2nd order method [5] provides an excellent trade off between sample quality and sampling speed.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [111]
- Not checked yetcites [5] source
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Empirical results demonstrate that adding a corrector based on Langevin Monte Carlo is more efficient than using an additional predictor without correctors [228].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [228]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“These deterministic ODE solvers typically converge much faster than their stochastic counterparts at the cost of slightly inferior sample quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.2 ODE Solvers.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Inspired by an analysis of DDIM on a singleton dataset, generalized Denoising Diffusion Implicit Models (gDDIM) [280] proposes a modified parameterization of the score network that enables deterministic sampling for more general diffusion processes, such as the one in Critically-Damped Langevin Diffusion (CLD) [59].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [280]
- Not checked yetcites [59]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Diffusion Exponential Integrator Sampler [279] and DPM-solver [145] leverage the semi-linear structure of probability flow ODE to develop customized ODE solvers that are more efficient than general-purpose Runge-Kutta methods.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [279]
- Not checked yetcites [145]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“However, it is well known that the variational lower bound used for DDPM training does not correlate directly with sample quality [235].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.1 Optimized Discretization.
What the sources say
- Not checked yetcites [235]
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“A subsequent work, called Differentiable Diffusion Sampler Search [246], addresses this issue by directly optimizing a common metric for sample quality called the Kernel Inception Distance (KID) [17].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.1 Optimized Discretization.
What the sources say
- Not checked yetcites [246]
- Not checked yetcites [17]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Heun's method generates samples of comparable, if not better quality than Euler's method with fewer sampling steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“One can improve sampling speed by truncating the forward and reverse diffusion processes [155,285].The key idea is to halt the forward diffusion process early on, after just a few steps, and to begin the reverse denoising process with a non-Gaussian distribution.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.2 Truncated Diffusion.
What the sources say
- Not checked yetcites [155]
- Not checked yetcites [285]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“By using partial steps or training a sampler for the reverse process, this method achieves faster sampling speeds at the expense of slight degradation in sample quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2 Learning-Based Sampling
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The higher-order solver leads to smaller discretization error at the cost of one additional evaluation of the learned score function per time step.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In Variational Diffusion Models (VDMs) [120], authors propose to improve the likelihood of continuous-time diffusion models by jointly training the noise schedule and other diffusion model parameters to maximize the VLB.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.1 Noise Schedule Optimization
What the sources say
- Not checked yetcites [120]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Samples from this distribution can be obtained efficiently by diffusing samples from pretrained generative models, such as variational autoencoders [122,194] or generative adversarial networks [71].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.2 Truncated Diffusion.
What the sources say
- Not checked yetcites [122]
- Not checked yetcites [194]
- Not checked yetcites [71]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Moreover, authors prove that the VLB for data point x can be simplified to a form that only depends on the signal-to-noise ratio R(t ) ᾱ 2 t σ 2 t .”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.1 Noise Schedule Optimization
What the sources say
- Not checked yetcites [120]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“By optimizing the forward noise schedule jointly with other parameters of diffusion models, one can further maximize the VLB in order to achieve higher loglikelihood values [120,165].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.1 Noise Schedule Optimization
What the sources say
- Not checked yetcites [120]
- Not checked yetcites [165]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As discussed in Section 2.1, the training objective for diffusion models is a (negative) variational lower bound (VLB) on the log-likelihood.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4 DIFFUSION MODELS WITH IMPROVED LIKELIHOOD
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“Specifically, in Progressive Distillation [201], the authors propose distilling the full sampling process into a faster sampler that requires only half as many steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.3 Knowledge Distillation.
What the sources say
- Not checked yetcites [201]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The work of iDDPM [165] demonstrates that a certain cosine noise schedule can improve loglikelihoods.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.1 Noise Schedule Optimization
What the sources say
- Not checked yetcites [165]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Approaches that use knowledge distillation [147,201] can significantly improve the sampling speed of diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.3 Knowledge Distillation.
What the sources say
- Not checked yetcites [147]
- Not checked yetcites [201]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The first part of Equation ( 37) is reminiscent of implicit score matching [98] and the whole bound can be efficiently estimated with Monte Carlo methods.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [98]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“One can also generate data by plugging the score model into the probability flow ODE in Equation ( 19), which gives:”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“D K L (q 0 p sde θ ) ≤ L(θ ; д(•) 2 ) + D K L (q T π ),(35)”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [222]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“log p ode θ (x 0 ) = log p T (x T ) + T t =0 ∇ • fθ (x t , t )dt .(38)”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Many methods propose to train the reverse variances as well to further maximize VLB and log-likelihood values.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.2 Reverse Variance Learning
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“One can compute the one-dimensional integral above with numerical ODE solvers and the Skilling-Hutchinson trace estimator [97,217].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Specifically, Song et al. (2021) [222] prove that with a special weighting function (likelihood weighting), the objective used for training score SDEs implicitly maximizes the expected value of p sde θ on data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [222]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“The theory of neural ODEs [34] and continuous normalizing flows [74] indicates that p ode θ can be computed accurately albeit with high computational cost.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [34]
- Not checked yetcites [74]
Strength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“To reduce the cost of directly maximizing p ode θ with the above formula, Song et al. (2021) [222] propose to maximize the variational lower bound of p sde θ as a proxy for maximizing p ode θ , giving rise to a family of diffusion models called ScoreFlows.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [222]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Since D K L (q 0 p sde θ ) = -E q 0 log(p sde θ ) + const, and D K L (q T π ) is a constant, training with L(θ ; д(•) 2 ) amounts to minimizing -E q 0 log(p sde θ ), the expected negative log-likelihood on data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Moreover, Song et al. (2021) and Huang et al. (2021) [95, 222] provide the following bound for p sde θ (x): log p sde θ (x) ≤ L (x),”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [95]
- Not checked yetcites [222]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Analytic-DPM [10] shows a remarkable result that the optimal reverse variance can be obtained from a pre-trained score function, with the analytic form below:”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.2 Reverse Variance Learning
What the sources say
- Not checked yetcites [10]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In the Score SDE [228] formulation, samples are generated by solving the following reverse SDE, where ∇ x t log p θ (x t , t ) in Equation ( 18) is replaced by the learned noise-conditional score model s θ (x t , t ):”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Unfortunately, this formula cannot be directly optimized to maximize p ode θ on data, as it requires calling expensive ODE solvers for each data point x 0 .”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“Lu et al. (2022) [144] further improve ScoreFlows by proposing to minimize not just the vanilla score matching loss function, but also its higher order generalizations.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [144]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“D3PM [6] accommodates discrete data in diffusion models by constructing the forward noising process with absorbing state kernels or discretized Gaussian kernels.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
What the sources say
- Not checked yetcites [6]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“To overcome this difficulty, several works [6,78,93,257] build on Sohl-Dickstein et al. (2015) [218] to generate discrete data of high dimensions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
What the sources say
- Not checked yetcites [6]
- Not checked yetcites [78] source
- Not checked yetcites [93]
- Not checked yetcites [257]
- Not checked yetcites [218]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“They prove that log p ode θ can be bounded with the first, second, and third-order score matching errors.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [144]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Campbell et al. (2022) [24] present the first continuous-time framework for discrete diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
What the sources say
- Not checked yetcites [24]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Niu et al. (2020) [169] first tackle the problem of permutation invariant graph generation with diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [169]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Similarly, Shi et al. (2021) [212] and Xu et al. (2021) [261] enable diffusion models to generate molecular conformations that are invariant to both translation and rotation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [212]
- Not checked yetcites [261]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, one can build a diffusion model that generates rotation and translation invariant molecular conformations as long as the prior and transition kernels enjoy the same invariance.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“Given that p(x T ) = p(T (x T )), p θ (x t -1 | x t ) = p θ (T (x t -1 ) | T (x t )), Xu et al. (2022) [261] prove that the distribution of samples is guaranteed to be invariant to T , that is, p 0 (x) = p 0 (T (x)).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [261]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“They achieve this by using a permutation equivariant graph neural network [72,206,254], called EDP-GNN, to parameterize the noise-conditional score model.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“To address this issue, several works [51,169] propose to endow diffusion models with the ability to account for invariance in data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [51]
- Not checked yetcites [169]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The RDM uses a variational lower bound (VLB) of the log-likelihood as its loss function.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [94]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“The Latent Score-Based Generative Model (LSGM) [238] seeks to address the problem of joint training by pairing a Score SDE diffusion model with a variational autoencoder (VAE) [122,194].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
- Not checked yetcites [122]
- Not checked yetcites [194]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The model also provides a formula for reversing diffusion on a manifold.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [51]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Taking an intrinsic view, the RSGM approximates the sampling process on Riemannian manifolds using a Geodesic Random Walk.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [51]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Recent studies have extended the Score SDE formulation to various known manifolds.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The Riemannian Score-Based Generative Model (RSGM) [51] accommodates a wide range of manifolds, including spheres and toruses, provided they satisfy mild conditions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [51]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In this configuration, the diffusion model is responsible for learning the prior distribution.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In contrast, the Riemannian Diffusion Model (RDM) [94] employs a variational framework to generalize the continuous-time diffusion model to Riemannian manifolds.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [94]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Consequently, identifying these manifolds and training diffusion models directly on them can be advantageous due to the lower data dimensionality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“The RSGM demonstrates that it is possible to extend diffusion models to compact Riemannian manifolds.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [51]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Additionally, the LSGM can manage discrete data by converting it into continuous latent codes.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The Latent Score-Based Generative Model (LSGM) [238] furthers this line of research by illustrating that the ELBO can be considered a specialized score matching objective in the context of latent space diffusion.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The DDPM can be conceptualized as a hierarchical Markovian VAE with a fixed encoder.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The authors of the LSGM propose a joint training objective that merges the VAE's evidence lower bound with the diffusion model's score matching objective.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“This results in a new lower bound for the data log-likelihood.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Though the cross-entropy term in the ELBO is intractable, it can be transformed into a tractable score matching objective by viewing the score-based generative model as an infinitely deep VAE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“By situating the diffusion model within the latent space, the LSGM achieves faster sample generation than conventional diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [238]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Rather than jointly training the autoencoder and diffusion model, the Latent Diffusion Model (LDM) [196] addresses each component separately.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [196] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In [120] demonstrate that the score matching objective may be approximated by the Evidence Lower Bound (ELBO) of a deep hierarchical VAE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
What the sources say
- Not checked yetcites [120]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“On the other hand, GAN can facilitate sampling speed of diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“However, the bijection requirement limits the modeling of complex data in both practical and theoretical contexts [44,249].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [44]
- Not checked yetcites [249]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although EBMs have a number of desirable properties, two challenges remain for modeling highdimensional data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Each EBM is trained with recovery likelihood, which aims to maximize the conditional probability of the data at a certain noise level, given their noisy versions at a higher noise level.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [69]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“In a recent study, Gao et al. (2020) [69] present a diffusion recovery likelihood method to tractably learn samples from a sequence of EBMs in the reverse process of the diffusion model.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [69]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“Instead of using causal masking on representations like ARMs, the ARDM is trained with an effective objective that mirrors that of diffusion probabilistic models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [92]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“recent work has shown that representations learned through DDPM contain high-level semantic information that is useful for segmentation tasks [11].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.2 Semantic Segmentation.
What the sources say
- Not checked yetcites [11]
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, such intermediate representations would lose some semantics in SGs.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.4.2 Image Generation Based on Scene Graphs.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIn the paper
“The Latent Diffusion Model (LDM) [196] streamlines the training and sampling processes for denoising diffusion models without sacrificing quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [196] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Existing methods [85,106,140] mainly predict an image-like layout from SGs, and then generate images based on the layout.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.4.2 Image Generation Based on Scene Graphs.
What the sources say
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“On the other hand, recent diffusion models [196] are not able to address this problem well.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.4.2 Image Generation Based on Scene Graphs.
What the sources say
- Not checked yetcites [196] source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the assumption that the forward process of diffusion models completely erases any information in data and renders it equivalent to a prior distribution may not always hold.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Revisiting Assumptions.
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, they cannot be easily used for tasks such as manipulating data based on semantic representations.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Latent Representations.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Rests on an assumption: Unlike variational autoencoders or generative adversarial networks, diffusion models are less effective for providing good representations of data in their latent space.
In the paper
“generate improper images [208]”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Pitfalls on Diffusion Models.
What the sources say
- Not checked yetcites [208] source
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“SGDiff can generate images that express complex relations in SGs better than both non-diffusion and diffusion methods.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.4.2 Image Generation Based on Scene Graphs.
What the sources say
- Not checked yetcites [268]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Adaptive Denoising Purification (ADP) [273] demonstrates that an EBM trained with denoising score matching [240] can effectively purify attacked images within just a few steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.5.1 Data Purification.
What the sources say
- Not checked yetcites [273]
- Not checked yetcites [240] source
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“adversarial purification has shown significant performance as an alternative defense method [273], which purifies attacked images into clean ones with a standalone purification model.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.5.1 Data Purification.
What the sources say
- Not checked yetcites [273]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“Sehwag et al. [209] and Um and Ye [237] enforce the generation process of the diffusion models to focus on minority samples such that they can generate high-fidelity samples from low-density regions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.5.2 Generating Synthetic Data for Robust Learning.
What the sources say
- Not checked yetcites [209] source
- Not checked yetcites [237]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“suffer from privacy issues [27]”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Pitfalls on Diffusion Models.
What the sources say
- Not checked yetcites [27]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
- It may state two separate claims as one. 66
- Probably not a substantial claim. 67
None of the sources cited for this claim have been checked yet.
In the paper
“and have also shown potential in a variety of domains, ranging from computer vision [2,11,19,23,88,90,113,115,134,150,160,173,198,200,248,270,271,283,290], natural language processing [6,93,139,205,275], temporal data modeling [1,33,124,191,233,262], multi-modal modeling [7,186,196,199,288], robust machine learning [18,28,112,242,273], to interdisciplinary applications in fields such as computa”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We clarify how they work under the same principle of diffusion and explain how these three models are connected and can be reduced to one another.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 1 INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Ho et al. (2020) [87] propose to reweight various terms in L VLB for better sample quality and noticed an important equivalence between the resulting loss function and the training objective for noise-conditional score networks (NCSNs), one type of score-based generative models, in Song and Ermon (2019) [223].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.1 Denoising Diffusion Probabilistic Models (DDPMs)
What the sources say
- Not checked yetcites [87]
- Not checked yetcites [223]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“This objective reduces to Equation (8) for a particular choice of the weighting function λ(t ), and has the same form as the loss of denoising score matching over multiple noise scales for training score-based generative models [223]”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.1 Denoising Diffusion Probabilistic Models (DDPMs)
What the sources say
- Not checked yetcites [223]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Training and sampling are completely decoupled in the formulation of score-based generative models, so one can use a multitude of sampling techniques after the estimation of score functions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.2 Score-Based Generative Models (SGMs)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both the reverse-time SDE and the probability flow ODE allow sampling from the same data distribution as their trajectories have the same marginals.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“The added velocity term is reported to improve sampling speed as well as quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [59]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Noise-Conditional Score Networks (NCSNs) [223] and Critically-Damped Langevin Diffusion (CLD) [59] both solve the reverse-time SDE with inspirations from Langevin dynamics.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [223]
- Not checked yetcites [59]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“The forward processes in DDPMs and SGMs are both discretizations of this SDE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Generating samples from diffusion models typically demands iterative approaches that involve a large number of evaluation steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3 DIFFUSION MODELS WITH EFFICIENT SAMPLING
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
In the paper
“Inspired by statistical mechanics, CLD proposes an augmented SDE with an auxiliary velocity term resembling underdamped Langevin diffusion.To obtain the time reversal of the extended SDE, CLD only needs to learn the score function of the conditional distribution of velocity given data, arguably easier than learning scores of data directly.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [59]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“This process can be applied to any types of forward SDEs, and empirical results indicate this sampler performs slightly better than DDPM [228] for a particular type of SDEs called the VP-SDE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Subsequent research on diffusion models focuses on improving these classical approaches (DDPMs, SGMs, and Score SDEs) from three major directions: faster and more efficient sampling, more accurate likelihood and density estimation, and handling data with special structures (such as permutation invariance, manifold structures, and discrete data).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 2.3 Stochastic Differential Equations (Score SDEs)
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Jolicoeur-Martineau et al. (2021) [107] develop an SDE solver with adaptive step sizes for faster generation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [107]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although the sampling trajectories of ALD are not exact solutions to the reverse-time SDE, they have the correct marginals and hence produce correct samples under the assumption that Langevin dynamics converges to its equilibrium at every noise level.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Langevin dynamics converges to its equilibrium at every noise level.
In the paper
“PNDM [142] proposes a pseudo numerical method to generate sample along a specific manifold in R N .It uses numerical solver with nonlinear transfer part to solve differential equation on manifolds and then generates sample, which encapsulates DDIM as a special case.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [142]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Karras et al. (2022) [111] further improve the Langevin dynamics corrector in [228] by proposing a Langevin-like “churn” step of adding and removing noise, achieving new state-of-the-art sample quality on datasets like CIFAR-10 [126] and ImageNet-64 [53].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [111]
- Not checked yetcites [228]
- Not checked yetcites [126]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“DDIM learns a Markov chain to reverse this non-Markov perturbation process, which is fully deterministic when σ 2 t = 0.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [220]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“It is observed in [111,145,201,220] that the DDIM sampling process amounts to a special discretization scheme of the probability flow ODE.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [111]
- Not checked yetcites [145]
- Not checked yetcites [201]
- Not checked yetcites [220]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The predictor-corrector method proposed in [228] solves the reverse SDE by combining numerical SDE solvers (“predictor”) and iterative Markov chain Monte Carlo (MCMC) approaches (“corrector”).”
- Also stated in: § 3.1.1 SDE Solvers. · plain
“The resulting samples have the same time-marginals as solution trajectories of the reverse-time SDE, i.e., they are equivalent in distribution at all time steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.1 SDE Solvers.
What the sources say
- Not checked yetcites [228]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Also stated in: § 3.1.1 SDE Solvers. · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In contrast to SDE solvers, the trajectories of ODE solvers are deterministic and thus not affected by stochastic fluctuations.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.1.2 ODE Solvers.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Based on truncated Taylor methods, Dockhorn et al. (2022) [60] derive a second-order solver for accelerating synthesis by training an additional head on top of the first-order score network.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.1 Optimized Discretization.
What the sources say
- Not checked yetcites [60]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Given a pre-trained diffusion model, Watson et al. (2021) [247] put forth a strategy for finding the optimal discretization scheme by selecting the best K time steps to maximize the training objective for DDPMs.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.1 Optimized Discretization.
What the sources say
- Not checked yetcites [247]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Key to this approach is the observation that the DDPM objective can be broken down into a sum of individual terms, making it well suited for dynamic programming.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.1 Optimized Discretization.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“These methods contain DDIM as a first-order approximation.However, they also allow for higher order integrators, which can produce highquality samples in just 10 to 20 iterations-far fewer than the hundreds of iterations typically required by diffusion models without accelerated sampling.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Denoising Diffusion Implicit Models (DDIM)
What the sources say
- Not checked yetcites [279]
- Not checked yetcites [145]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Repeating this procedure can further reduce sampling steps, although fewer steps can result in reduced sample quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 3.2.3 Knowledge Distillation.
What the sources say
- Not checked yetcites [201]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“This bound, however, may not be tight in many cases [120], leading to potentially suboptimal log-likelihoods from diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4 DIFFUSION MODELS WITH IMPROVED LIKELIHOOD
What the sources say
- Not checked yetcites [120]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, noise schedules do not affect the VLB as long as they share the same values at R min and R max , and will only affect the variance of Monte Carlo estimators for VLB.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.1 Noise Schedule Optimization
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, given a pre-trained score model, we can estimate its first-and second-order moments to obtain the optimal reverse variances.Plugging them into the VLB can lead to tighter VLBs and higher likelihood values.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.2 Reverse Variance Learning
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“In iDDPM [165], Nichol and Dhariwal propose to learn the reverse variances by parameterizing them with a form of linear interpolation and training them using a hybrid objective.This results in higher log-likelihoods and faster sampling without losing sample quality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.2 Reverse Variance Learning
What the sources say
- Not checked yetcites [165]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The classical formulation of diffusion models assumes that Gaussian transition kernels in the reverse Markov chain have fixed variance parameters.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.2 Reverse Variance Learning
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“For p sde θ , several concurrent works [95,144,222] demonstrate that there exists an efficiently computable variational lower bound, and we can directly train our diffusion models to maximize p sde θ using modified diffusion losses.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [95]
- Not checked yetcites [144]
- Not checked yetcites [222]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Since the probability flow ODE is a special case of neural ODEs or continuous normalizing flows, we can use well-established approaches in those fields to compute log p ode θ accurately.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Difficulties may arise, for example, when models rely on score functions that are only defined on continuous data domains, or when data reside on low dimensional manifolds.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5 DIFFUSION MODELS FOR DATA WITH SPECIAL STRUCTURES
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Most diffusion models are geared towards continuous data domains, because Gaussian noise perturbation as used in DDPMs is not a natural fit for discrete data, and the score functions required by SGMs and Score SDEs are only defined on continuous data domains.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Leveraging Continuous Time Markov Chains, they are able to derive efficient samplers that outperform discrete counterparts, while providing a theoretical analysis on the error between the sample distribution and the true data distribution.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
What the sources say
- Not checked yetcites [24]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Specifically, VQ-Diffusion [78] replaces Gaussian noise with a random walk on the discrete data space, or a random masking operation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.1 Discrete Data
What the sources say
- Not checked yetcites [78] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Building upon this theoretical result, authors further propose efficient training algorithms for minimizing high order score matching losses and reported improved p ode θ on data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 4.3 Exact Likelihood Computation
What the sources say
- Not checked yetcites [144]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While diffusion models have achieved great success for data domains like images and audio, they do not necessarily translate seamlessly to other modalities.Many important data domains have special structures that must be taken into account for diffusion models to function effectively.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5 DIFFUSION MODELS FOR DATA WITH SPECIAL STRUCTURES
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Data in many important domains have invariant structures.For example, graphs are permutation invariant, and point clouds are both translation and rotation invariant.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“For example, Xu et al. (2022) [261] shows that Markov chains starting with an invariant prior and evolving with equivariant Markov kernels can induce an invariant marginal distribution, which can be used to enforce appropriate data invariance in molecular conformation generation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [261]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“This process models both the joint distribution of nodes and edges through a system of stochastic differential equations (SDEs), where message-passing operations are used to guarantee permutation invariance.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [105]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In diffusion models, these invariances are often ignored, which can lead to suboptimal performance.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“GDSS [105] further develops this idea by proposing a continuous-time graph diffusion process.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.2 Data with Invariant Structures
What the sources say
- Not checked yetcites [105]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In order to be successful, it is crucial to design a loss function that allows for the joint training of the autoencoder and the diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“Unlike the RSGM, the RDM takes an extrinsic view, assuming that the relevant Riemannian manifold is embedded in a higher dimensional Euclidean space.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [94]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Many recent works have built on this idea, starting by using an autoencoder to condense the data into a lower dimensional manifold, followed by training diffusion models in this latent space.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The authors of the RDM model have shown that maximizing this VLB is equivalent to minimizing a Riemannian scorematching loss.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [94]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In addition, many data domains have well-known manifold structures.For instance, climate and earth data naturally lie on the sphere because that is the shape of our planet.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3 Data with Manifold Structures
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“According to the manifold hypothesis [66], most natural data lies on manifolds with significantly reduced intrinsic dimensionality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [66] source
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“This adaptation parallels the generalization of neural ODEs [34] and continuous normalizing flows [74] to Riemannian manifolds [143,157].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [34]
- Not checked yetcites [74]
- Not checked yetcites [143]
- Not checked yetcites [157]
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Data with manifold structures are ubiquitous in machine learning.As the manifold hypothesis [66] posits, natural data often reside on manifolds with lower intrinsic dimensionality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3 Data with Manifold Structures
What the sources say
- Not checked yetcites [66] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“It is trained with a generalized denoising score matching objective.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.1 Known Manifolds.
What the sources say
- Not checked yetcites [51]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In these cases, the manifold is implicitly defined by the autoencoder and learned through the reconstruction loss.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This formulation allows flexible choice of encoder and decoder models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Typically, these models are represented by exponential family distributions whose parameters are generated by multi-layer neural networks.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
None of the sources cited for this claim have been checked yet.
In the paper
“Variational Autoencoders [61,123,194] aim to learn both an encoder and a decoder to map input data to values in a continuous latent space.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
What the sources say
- Not checked yetcites [61]
- Not checked yetcites [123] source
- Not checked yetcites [194]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“First, an autoencoder is trained to produce a low-dimensional latent space.Then, the diffusion model is trained to generate latent codes.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [196] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Specifically, DDPM's forward process functions as the encoder, and this process is structured as a linear Gaussian model (as described by Equation ( 2)).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“To guarantee an effective inference, a variational Bayes approach is used to maximize the evidence lower bound:”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The latent variables within the decoder are all the same size as the sample data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“DALLE-2 [186] employs a similar strategy by training a diffusion model on the CLIP image embedding space, followed by training a separate decoder to create images based on the CLIP image embeddings.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 5.3.2 Learned Manifolds.
What the sources say
- Not checked yetcites [186]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Consequently, optimizing a diffusion model can be seen as training an infinitely deep hierarchical VAE-a finding that supports the common belief that Score SDE diffusion models can be interpreted as the continuous limit of hierarchical VAEs.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The DDPM's reverse process, on the other hand, corresponds to the decoder, which is shared across multiple decoding steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Provided that the parameterized likelihood function p θ (x | z) and the parameterized posterior approximation q ϕ (z | x) can be computed in a point-wise way and are differentiable with their parameters, the ELBO can be maximized with gradient descent.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In these models, the embedding can be interpreted as a latent variable in a probabilistic generative model, and a probabilistic decoder can be formulated by a parameterized likelihood function.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.1 Variational Autoencoders and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Namely, the goal of GAN optimization is to achieve Nash equilibrium [192].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
What the sources say
- Not checked yetcites [192] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Taking advantage of the flexible diffusion model, Wang et al. (2022) [245] inject noise to the discriminator with an adaptive noise schedule determined by a diffusion model.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
What the sources say
- Not checked yetcites [245]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The optimization of GANs can be viewed as a minimax optimization problem with value function V (G, D):”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Xiao et al. (2021) [256] show that slow sampling is caused by the Gaussian assumption in the denoising step, which is justified only for small step sizes.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
What the sources say
- Not checked yetcites [256]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The generator G aims to generate new examples and implicitly model the data distribution.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“One solution is to inject noise into the discriminator input for widening the support of both the generator and discriminator distributions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Normalizing flows can transform simple probability distribution into an extremely complex probability distribution, which can be used in generative models, reinforcement learning, variational inference, and other fields.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“As such, each denoising step is modeled by a conditional GAN, allowing larger step size.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
What the sources say
- Not checked yetcites [256]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“At that point, the generator can be considered that it has captured the accurate distribution of real examples.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Generative Adversarial Networks (GANs) [45,71,79] mainly consist of two models: a generator G and a discriminator D.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
What the sources say
- Not checked yetcites [45] source
- Not checked yetcites [71]
- Not checked yetcites [79]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The discriminator D is usually a binary classifier that is used to identify generated examples from true examples with maximally possible accuracy.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Normalizing flows [56,193] are generative models that generate tractable distributions to model high-dimensional data [57,121].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [56]
- Not checked yetcites [193]
- Not checked yetcites [57]
- Not checked yetcites [121]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“One of the issues of GAN is the instability in the training process, which is mainly caused by the non-overlapping between the distribution of input data and that of the generated data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The optimization process ends at a saddle point that produces a minimum about the generator and a maximum about the discriminator.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.2 Generative Adversarial Networks and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The trajectory in normalizing flows is formulated by a differential equation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Similar to the continuous setting, normalizing flows allow for the retrieval of the exact loglikelihood through a change of variable formula.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“For example, DiffFlow [278] introduces a generative modeling algorithm that combines the benefits of both flow-based and diffusion models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [278]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Autoregressive Models (ARMs) work by decomposing the joint distribution of data into a product of conditional distributions using the probability chain rule:”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [13] source
- Not checked yetcites [127]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Existing normalizing flows are constructed based on the change of variable formula [56,193].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [56]
- Not checked yetcites [193]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“As a result, DiffFlow produces sharper boundaries than normalizing flow and learns more general distributions with fewer discretization steps compared to diffusion probabilistic models.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [278]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Several works attempt to relax this bijection requirement [57,249].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
What the sources say
- Not checked yetcites [57]
- Not checked yetcites [249]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Recent advances in deep learning have facilitated significant progress for various data modalities [29,161,205], such as images [38,239], audio [110,170], and text [14,20,75,159,162].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [29] source
- Not checked yetcites [161]
- Not checked yetcites [205]
- Not checked yetcites [38]
- Not checked yetcites [239]
- Not checked yetcites [110]
- Not checked yetcites [170]
- Not checked yetcites [14]
- Not checked yetcites [20]
- Not checked yetcites [75]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the discrete-time setting, the mapping from data x to latent z in normalizing flows is a composition of a sequence of bijections, taking the form of F = F N • F N -1 • . . .• F 1 .”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.3 Normalizing Flows and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“An energy-based model is defined as p θ (x) = 1 Z θ exp( f θ (x)), where Z θ = exp( f θ (x))dx is the partition function, which is analytically intractable for high-dimensional x.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“First, learning EBMs by maximizing the likelihood requires MCMC method to generate samples from the model, which can be very computationally expensive.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Sampling from these models requires the same number of network calls as the data's dimensionality.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The Autoregressive Diffusion Model (ARDM) [92], on the other hand, is capable of generating arbitrary-order data, including order-agnostic autoregressive models and discrete diffusion models as special cases [6,93,219].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [92]
- Not checked yetcites [6]
- Not checked yetcites [93]
- Not checked yetcites [219]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Energy-based Models (EBMs) [119,129,226] can be viewed as one generative version of discriminators [101,128,131], while can be learned from unlabeled input data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While ARMs are effective density estimators, sampling is a continuous, time-consuming process-particularly for high-dimensional data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For images, f θ (x) is parameterized by a convolutional neural network with a scalar output.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Second, as demonstrated in [168], the energy potentials learned with non-convergent MCMC are not stable, in the sense that samples from long-run Markov chains can be significantly different from the observed samples, and thus it is difficult to evaluate the learned energy potentials.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [168]
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Salimans and Ho (2021) [202] compare both constrained score models and energy-based models for modeling the score of the data distribution, finding that constrained score models, i.e., energy based models, can perform just as well as unconstrained models when using a comparable model structure.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [202]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“At the testing stage, the ARDM is able to generate data in parallel-enabling its application to a range of arbitrary-generation tasks.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [92]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Autoregressive models (ARMs) offer generative capabilities through the use of a single neural network.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.4 Autoregressive Models and Connections with Diffusion Models
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“For example, the Flexible Diffusion Model (FDM) [83] uses a generative model to allow for the sampling of any arbitrary subset of video frames, given any other subset.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.3 Video Generation.
What the sources say
- Not checked yetcites [83]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“EBMs maximize the recovery likelihood because it is more tractable than marginal likelihood, as sampling from the conditional distributions is much easier than sampling from the marginal distributions.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“For inpainting tasks, RePaint [146] features an enhanced denoising strategy that uses resampling iterations to better condition the image (see Figure 5).”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [146] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“SDEdit [160] uses a Stochastic Differential Equation (SDE) prior to improve fidelity.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [160]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Meanwhile, Palette [198] employs conditional diffusion models to create a unified framework for four image generation tasks: colorization, inpainting, uncropping, and JPEG restoration.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [198] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“SR3 conducts super-resolution through a stochastic, iterative denoising process.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [200] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The Cascaded Diffusion Model (CDM) [88] consists of multiple diffusion models in sequence, each generating images of increasing resolution.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [88]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“This model can generate high-quality samples, and long-run MCMC samples from the conditional distributions still resemble realistic images.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 6.5 Energy-based Models and Connections with Diffusion Models
What the sources say
- Not checked yetcites [69]
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Both the SR3 and CDM directly apply the diffusion process to input images, which leads to larger evaluation steps.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [200] source
- Not checked yetcites [88]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Similarly, Decoder Denoising Pretraining (DDeP) [19] integrates diffusion models with denoising autoencoders [241] and delivers promising results on label-efficient semantic segmentation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.2 Semantic Segmentation.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Super-Resolution via Repeated Refinement (SR3) [200] uses DDPM to enable conditional image generation.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.1.1 Super Resolution, Inpainting, and Translation.
What the sources say
- Not checked yetcites [200] source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“diffusion models would learn and even amplify the bias in the training dataset [21,39]”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Pitfalls on Diffusion Models.
What the sources say
- Not checked yetcites [21]
- Not checked yetcites [39]
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“In addition, some approaches apply guided diffusion processes for advanced adversarial purification [242,251].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.5.1 Data Purification.
What the sources say
- Not checked yetcites [242]
- Not checked yetcites [251]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“GeoDiff [261] demonstrates that Markov chains evolving with equivariant Markov kernels can produce an invariant distribution, and further designs blocks for the Markov kernels to preserve the desirable equivariance property”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.6.1 Molecular Graph Modeling.
What the sources say
- Not checked yetcites [261]
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Furthermore, since the latent space in diffusion models often possesses the same dimensionality as the data space, sampling efficiency is negatively affected and the models may not learn the representation schemes well [103].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Latent Representations.
What the sources say
- Not checked yetcites [103]
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Wang et al. [244] employ the recent diffusion model to improve adversarial training, and the trained models achieve state-ofthe-art performance using only generated data.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.5.2 Generating Synthetic Data for Robust Learning.
What the sources say
- Not checked yetcites [244]
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Recent advances in Schrödinger bridges and optimal transport [35,50,52,214,221] provide promising alternative solutions, suggesting new formulations for diffusion models that are capable of converging to a specified prior distribution in finite time.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Revisiting Assumptions.
What the sources say
- Not checked yetcites [35]
- Not checked yetcites [50]
- Not checked yetcites [52]
- Not checked yetcites [214]
- Not checked yetcites [221]
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Other methods incorporate the equivariance property into 3D molecule generation [91] and protein generation [3,15].”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > 7.6.1 Molecular Graph Modeling.
What the sources say
- Not checked yetcites [91]
- Not checked yetcites [3]
- Not checked yetcites [15] source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In reality, complete removal of information is unachievable in finite time.”
§ Diffusion Models: A Comprehensive Survey of Methods and Applications > Revisiting Assumptions.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. The paper may give no reason why it holds.
The paper relies on this without support.
Over the past two years, the body of research on diffusion models has grown significantly, making it increasingly challenging for new researchers to stay abreast of recent developments.
“Over the past two years, the body of research on diffusion models has grown significantly, making it increasingly challenging for new researchers to stay abreast of the recent developments in the field.”
The paper relies on this without support.
The sheer volume of work on diffusion models can obscure major trends and hinder further research progress.
“Additionally, the sheer volume of work can obscure major trends and hinder further research progress.”
The authors state this as an assumption.
Langevin dynamics converges to its equilibrium at every noise level.
“under the assumption that Langevin dynamics converges to its equilibrium at every noise level”
The paper relies on this without support.
Text-to-image generation models struggle to faithfully reproduce complex sentences with many objects and relationships.
“Despite text-to-image generation models have made significant progress, they struggle to faithfully reproduce complex sentences with many objects and relationships.”
The paper relies on this without support.
High-quality paired scene-graph-image datasets are scarce.
“However, highquality paired SG-image datasets are scarce.”
The paper relies on this without support.
Diffusion models have emerged as a powerful framework, notably as the only one that can rival generative adversarial networks in most applications without resorting to adversarial training.
“Diffusion models have emerged as a powerful framework, notably as the only one that can rival generative adversarial networks (GANs) in most applications without resorting to adversarial training.”
The paper relies on this without support.
Unlike variational autoencoders or generative adversarial networks, diffusion models are less effective for providing good representations of data in their latent space.
“Unlike variational autoencoders or generative adversarial networks, diffusion models are less effective for providing good representations of data in their latent space.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“Their ability to produce photorealistic imagery with fine-grained control has made them the dominant tools for generating synthetic content (Yang et al. 2023), including AI CSAM (Thorn 2024a).”
From AI-generated child sexual abuse material: what’s the harm? (2026) · cites this paper as Yang et al. 2023
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Grad-TTS2 name disagrees with its cited reference
MinorThe text calls the model Grad-TTS2, but reference [118] is titled Guided-TTS 2.
“Grad-TTS2 [118] improves Grad-TTS in an adaptive way.”
“118. Sungwon Kim, Heeseung Kim, and Sungroh Yoon. 2022. Guided-TTS 2: A diffusion model for high-quality adaptive text-to-speech with untranscribed data.”
Latent Diffusion Models is cited as DPM-solver
MinorThe citation attached to Latent Diffusion Models points to a bibliography entry for DPM-solver, not the paper identified elsewhere in the text as LDM [196].
“Latent Diffusion Models [145]”
“145. Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. 2022. DPM-solver: A fast ODE solver for diffusion probabilistic model sampling in around 10 steps.”
GeoDiff citation year disagrees with the reference
MinorThe text dates reference [261] to 2022, while its bibliography entry gives 2021.
“Xu et al. (2022) [261] shows that Markov chains starting with an invariant prior and evolving with equivariant Markov kernels can induce an invariant marginal distribution”
“261. Minkai Xu, Lantao Yu, Yang Song, Chence Shi, Stefano Ermon, and Jian Tang. 2021. GeoDiff: A geometric diffusion model for molecular conformation generation.”
DDPM reverse SDE has the opposite score-term sign
MinorEquation (18) subtracts the score term in a reverse-time SDE. Substituting the DDPM drift from Equation (16) therefore gives a negative score term, but Equation (21) gives it a positive sign.
“dx = - 1 2 β (t )(x t -∇ x t log q t (x t ))dt + β (t )dw(21)”
“dx = f (x, t ) -д(t ) 2 ∇ x log q t (x) dt + д(t )d w (18”
Annealed Langevin sampling uses incompatible time-step ranges
MinorThe stated iteration runs from T down to 1, but the immediately following initialization rule applies from 0 up to T−1. As written, the rule does not initialize the first stated step, t = T, and the stated iteration does not perform the t = 0 step.
“We first initialize ALD with x (N ) T ∼ N (0, I), then apply Langevin Monte Carlo for t = T ,T -1, • • • , 1 one after the other.”
“At each time step 0 ≤ t < T , we start with x (0) t = x (N ) t +1”
Citations
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Metadata
- Authors
- Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Zhang, W., Cui, B., & Yang, M.-H.
- Affiliations
- Peking University (CN)
- OpenAI (United States) (US)
- University of California, Los Angeles (US)
- University of Southern California (US)
- HEC Montréal (CA)
- University of California, Merced (US)
- ORCID
- Venue
- ACM Computing Surveys
- Published
- 2023-11-09
- Volume
- 56
- Issue
- 4
- Pages
- 1-39
- ISSN
- 0360-0300 (ISSN-L)
- 1557-7341
- OpenAlex
- W4387195417
- Cited by
- 1,704
- References
- 199
- Citations by year
- 2026: 392 · 2025: 683 · 2024: 483 · 2023: 142
- FWCI
- 154.02
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Computing Surveys (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Generative Adversarial Networks and Image Synthesis
- Physical Sciences › Computer Science › Artificial Intelligence › Adversarial Robustness in Machine Learning
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Keywords
- diffusion models, deep generative models, efficient sampling, likelihood estimation, structured data, hybrid generative models, image generation, video generation, temporal data modeling
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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