REVIEW 19 cited by
Convergence of denoising diffusion models under the manifold hypothesis
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Convergence of denoising diffusion models under the manifold hypothesis
read the original abstract
Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a reference density, which is usually Gaussian. Despite their strong empirical results, the theoretical analysis of such models remains limited. In particular, all current approaches crucially assume that the target density admits a density w.r.t. the Lebesgue measure. This does not cover settings where the target distribution is supported on a lower-dimensional manifold or is given by some empirical distribution. In this paper, we bridge this gap by providing the first convergence results for diffusion models in this more general setting. In particular, we provide quantitative bounds on the Wasserstein distance of order one between the target data distribution and the generative distribution of the diffusion model.
Forward citations
Cited by 19 Pith papers
-
An exact information theory of generalization phase transitions in Bayesian diffusion models
Bayesian diffusion models memorize training data when mutual information between restricted observations and training data exceeds log dataset size, and generalize otherwise.
-
Asymptotic-Preserving A Posteriori Analysis of Diffusion and Flow-Matching Samplers
DDIM (σ-clock Euler) is the unique layer-exact fixed-step sampler; deterministic residual budgets stay O(1) with no log(1/σ_min), while stochastic path-KL scales as Λ²/N from the Itô term alone.
-
Let EEG Models Learn EEG
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising me...
-
Training-Free Generative Sampling via Moment-Matched Score Smoothing
MM-SOLD is a training-free particle sampler whose large-particle limit converges to a moment-matched Gibbs distribution obtained by exponentially tilting a score-smoothed target.
-
Proximal-Based Generative Modeling for Bayesian Inverse Problems
PGM replaces the intractable likelihood score in diffusion models with a closed-form Moreau score computed via proximal operators, enabling non-asymptotic sampling for inverse problems trained only on prior data.
-
Proximal-Based Generative Modeling for Bayesian Inverse Problems
PGM framework links diffusion to proximal regularization for closed-form Moreau-score sampling in Bayesian inverse problems, learned only from prior samples.
-
The tractability landscape of diffusion alignment: regularization, rewards, and computational primitives
The choice of closeness measure in diffusion reward alignment determines the computational primitives and tractable reward classes, with linear exponential tilts sufficing for KL with convex rewards and proximal oracl...
-
Geometry-Aware Discretization Error of Diffusion Models
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
-
Diffusion Processes on Implicit Manifolds
Implicit Manifold-valued Diffusions (IMDs) are data-driven SDEs built from proximity graphs that converge in law to smooth manifold diffusions as sample count increases.
-
Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and p...
-
Structured drift design for denoising diffusion models
A variance-aware anisotropic OU drift keeps multimodal and correlated structure longer in diffusion, and bounds reverse initialization error by local cluster variance rather than global variance.
-
Noise Schedule Design for Diffusion Models: An Optimal Control Perspective
Recasting diffusion noise schedule design as optimal control on Fisher information yields sufficient conditions for O(d/n) sampling error and parametric closed-form schedules that generalize exponential/sigmoid ones a...
-
Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
-
Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
Diffusion-based denoising score matching avoids the mode-separation degradation that affects vanilla score matching error bounds, via suitable hyperparameter choice.
-
On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures
The paper proves Hölder continuity of optimal transport maps for PDE-induced measures via doubling conditions and derives excess-risk bounds for one-step generative models like DeepParticle.
-
On the Limits of Latent Reuse in Diffusion Models
Reusing source latent spaces in diffusion models under distribution shift produces target score error set by principal-angle misalignment and diffusion-time-amplified ambient noise.
-
Structured drift design for denoising diffusion models
Proposes GOU process with anisotropic drift to embed data geometry in diffusion models, claiming better mode separation, correlation preservation, and convergence than isotropic baselines.
-
Statistical Properties of Training & Generalization
Neural scaling laws in deep learning interact with physics constraints and inductive biases beyond classical statistics.
-
Statistical Properties of Training & Generalization
Review of neural scaling laws and their relation to constraints and inductive biases when applying machine learning to physics problems.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.