Understanding DDPM Latent Codes Through Optimal TransportDownload PDF

Published: 01 Feb 2023, Last Modified: 12 Mar 2024ICLR 2023 posterReaders: Everyone
Keywords: diffusion models, ddpm, optimal transport, theory
Abstract: Diffusion models have recently outperformed alternative approaches to model the distribution of natural images. Such diffusion models allow for deterministic sampling via the probability flow ODE, giving rise to a latent space and an encoder map. While having important practical applications, such as the estimation of the likelihood, the theoretical properties of this map are not yet fully understood. In the present work, we partially address this question for the popular case of the VP-SDE (DDPM) approach. We show that, perhaps surprisingly, the DDPM encoder map coincides with the optimal transport map for common distributions; we support this claim by extensive numerical experiments using advanced tensor train solver for multidimensional Fokker-Planck equation. We provide additional theoretical evidence for the case of multivariate normal distributions.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Generative models
TL;DR: ddim encoder is almost equal to optimal transport
Supplementary Material: zip
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](https://www.catalyzex.com/paper/arxiv:2202.07477/code)
26 Replies