A Flexible Diffusion Model

Weitao Du, He Zhang, Tao Yang, Yuanqi Du
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:8678-8696, 2023.

Abstract

Denoising diffusion (score-based) generative models have become a popular choice for modeling complex data. Recently, a deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been established, leading to the development of new SDE variants such as sub-VP and critically-damped Langevin. Despite the empirical success of some hand-crafted forward SDEs, many potentially promising forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing diffusion models, particularly the spatial part of forward SDEs, by leveraging the symplectic and Riemannian geometry of the data manifold. We introduce a systematic formalism with theoretical guarantees and connect it with previous diffusion models. Finally, we demonstrate the theoretical advantages of our method from a variational optimization perspective. We present numerical experiments on synthetic datasets, MNIST and CIFAR10 to validate the effectiveness of our framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-du23g, title = {A Flexible Diffusion Model}, author = {Du, Weitao and Zhang, He and Yang, Tao and Du, Yuanqi}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {8678--8696}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/du23g/du23g.pdf}, url = {https://proceedings.mlr.press/v202/du23g.html}, abstract = {Denoising diffusion (score-based) generative models have become a popular choice for modeling complex data. Recently, a deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been established, leading to the development of new SDE variants such as sub-VP and critically-damped Langevin. Despite the empirical success of some hand-crafted forward SDEs, many potentially promising forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing diffusion models, particularly the spatial part of forward SDEs, by leveraging the symplectic and Riemannian geometry of the data manifold. We introduce a systematic formalism with theoretical guarantees and connect it with previous diffusion models. Finally, we demonstrate the theoretical advantages of our method from a variational optimization perspective. We present numerical experiments on synthetic datasets, MNIST and CIFAR10 to validate the effectiveness of our framework.} }
Endnote
%0 Conference Paper %T A Flexible Diffusion Model %A Weitao Du %A He Zhang %A Tao Yang %A Yuanqi Du %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-du23g %I PMLR %P 8678--8696 %U https://proceedings.mlr.press/v202/du23g.html %V 202 %X Denoising diffusion (score-based) generative models have become a popular choice for modeling complex data. Recently, a deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been established, leading to the development of new SDE variants such as sub-VP and critically-damped Langevin. Despite the empirical success of some hand-crafted forward SDEs, many potentially promising forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing diffusion models, particularly the spatial part of forward SDEs, by leveraging the symplectic and Riemannian geometry of the data manifold. We introduce a systematic formalism with theoretical guarantees and connect it with previous diffusion models. Finally, we demonstrate the theoretical advantages of our method from a variational optimization perspective. We present numerical experiments on synthetic datasets, MNIST and CIFAR10 to validate the effectiveness of our framework.
APA
Du, W., Zhang, H., Yang, T. & Du, Y.. (2023). A Flexible Diffusion Model. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:8678-8696 Available from https://proceedings.mlr.press/v202/du23g.html.

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