Theoretical insights for diffusion guidance: A case study for Gaussian mixture models

Yuchen Wu, Minshuo Chen, Zihao Li, Mengdi Wang, Yuting Wei
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:53291-53327, 2024.

Abstract

Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text input is encoded as guidance to generate semantically aligned images. Proper guidance inputs are closely tied with the performance of diffusion models. A common observation is that strong guidance promotes a tight alignment to the task-specific information, while reduces the diversity of the generated samples. In this paper, we provide the first theoretical study towards the influence of guidance on diffusion models in the context of Gaussian mixture models. Under mild conditions, we prove that incorporating diffusion guidance not only boosts prediction confidence but also diminishes distribution diversity, leading to a reduction in the differential entropy of the output distribution. Our analysis covers the widely used DDPM and DDIM sampling schemes, and leverages comparison inequalities in differential equations as well as the Fokker-Planck equation that characterizes the evolution of probability density function, which may be of independent theoretical interest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-wu24b, title = {Theoretical insights for diffusion guidance: A case study for {G}aussian mixture models}, author = {Wu, Yuchen and Chen, Minshuo and Li, Zihao and Wang, Mengdi and Wei, Yuting}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {53291--53327}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/wu24b/wu24b.pdf}, url = {https://proceedings.mlr.press/v235/wu24b.html}, abstract = {Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text input is encoded as guidance to generate semantically aligned images. Proper guidance inputs are closely tied with the performance of diffusion models. A common observation is that strong guidance promotes a tight alignment to the task-specific information, while reduces the diversity of the generated samples. In this paper, we provide the first theoretical study towards the influence of guidance on diffusion models in the context of Gaussian mixture models. Under mild conditions, we prove that incorporating diffusion guidance not only boosts prediction confidence but also diminishes distribution diversity, leading to a reduction in the differential entropy of the output distribution. Our analysis covers the widely used DDPM and DDIM sampling schemes, and leverages comparison inequalities in differential equations as well as the Fokker-Planck equation that characterizes the evolution of probability density function, which may be of independent theoretical interest.} }
Endnote
%0 Conference Paper %T Theoretical insights for diffusion guidance: A case study for Gaussian mixture models %A Yuchen Wu %A Minshuo Chen %A Zihao Li %A Mengdi Wang %A Yuting Wei %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-wu24b %I PMLR %P 53291--53327 %U https://proceedings.mlr.press/v235/wu24b.html %V 235 %X Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text input is encoded as guidance to generate semantically aligned images. Proper guidance inputs are closely tied with the performance of diffusion models. A common observation is that strong guidance promotes a tight alignment to the task-specific information, while reduces the diversity of the generated samples. In this paper, we provide the first theoretical study towards the influence of guidance on diffusion models in the context of Gaussian mixture models. Under mild conditions, we prove that incorporating diffusion guidance not only boosts prediction confidence but also diminishes distribution diversity, leading to a reduction in the differential entropy of the output distribution. Our analysis covers the widely used DDPM and DDIM sampling schemes, and leverages comparison inequalities in differential equations as well as the Fokker-Planck equation that characterizes the evolution of probability density function, which may be of independent theoretical interest.
APA
Wu, Y., Chen, M., Li, Z., Wang, M. & Wei, Y.. (2024). Theoretical insights for diffusion guidance: A case study for Gaussian mixture models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:53291-53327 Available from https://proceedings.mlr.press/v235/wu24b.html.

Related Material