REVIEW 6 cited by
Low-dimensional adaptation of diffusion models: Convergence in total variation
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
Low-dimensional adaptation of diffusion models: Convergence in total variation
read the original abstract
This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion probabilistic model (DDPM), we prove that their iteration complexities under exact score functions are at most the order of $k/\varepsilon$ (up to log factor), where $\varepsilon$ is the precision in total variation distance and $k$ is some intrinsic dimension of the target distribution. We further extend these convergence guarantees to the setting in which the score functions are learned from data rather than known exactly, showing that the convergence performance degrades gracefully under suitable score estimation assumptions. We then show that these assumptions are attainable via kernel-based score estimators with finite-sample guarantees that also adapt to the low-dimensional structure. Our results apply to a broad family of target distributions without requiring smoothness or log-concavity. Our findings provide the first rigorous evidence for the adaptivity of the DDIM-type samplers to unknown low-dimensional structure, and improve over the state-of-the-art DDPM theory regarding total variation convergence.
Forward citations
Cited by 6 Pith papers
-
Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs
Transformers converge globally to the optimal DDPM denoiser for multi-token GMMs via self-attention mean denoising, with explicit token and iteration requirements.
-
When Diffusion Model Can Ignore Dimension: An Entropy-Based Theory
For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
-
Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
-
On the Robustness of Distribution Support under Diffusion Guidance
Guided diffusion generates samples near the target distribution support under exact score access, explaining its empirical success in producing plausible outputs.
-
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.
-
On the Robustness of Distribution Support under Diffusion Guidance
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.