2024-09-12-deng24b.md

title	abstract	openreview	section	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Reflected Schrödinger Bridge for Constrained Generative Modeling	Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrödinger Bridge algorithm{—}an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence{—}a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.	8Wl7xRXUHK	Papers	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	deng24b	0	Reflected Schrödinger Bridge for Constrained Generative Modeling	1055	1082	1055-1082	1055	false	Deng, Wei and Chen, Yu and Yang, Nicole Tianjiao and Du, Hengrong and Feng, Qi and Chen, Ricky Tian Qi	given family Wei Deng given family Yu Chen given family Nicole Tianjiao Yang given family Hengrong Du given family Qi Feng given family Ricky Tian Qi Chen	2024-09-12		Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence	244	inproceedings	date-parts 2024 9 12	https://raw.githubusercontent.com/mlresearch/v244/main/assets/deng24b/deng24b.pdf