Reverse-time diffusion processes in discrete time

Soura Dasgupta; Brian D. O. Anderson

doi:10.1109/CDC57313.2025.11312217

Reverse-time diffusion processes in discrete time

Soura Dasgupta, Brian D. O. Anderson

School of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

Abstract

Generative AI relies on finding reverse models for linear discrete time forward diffusions with non-Gaussian initial states, but uses indirect methods for reversal as there is no theory for direct reversal in discrete time. We give sufficient conditions that guarantee the existence of a reverse time diffusion and give a method of meeting them. We also give
a necessary and sufficient condition for the reverse model to be input-affine.

Original language	English
Title of host publication	Proceedings of 64th IEEE Conference on Decision and Control
Publisher	IEEE
Pages	5487-5492
Number of pages	6
ISBN (Electronic)	979-8-3315-2627-6
DOIs	https://doi.org/10.1109/CDC57313.2025.11312217
Publication status	Published - Dec 2025

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10.1109/CDC57313.2025.11312217

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title = "Reverse-time diffusion processes in discrete time",

abstract = "Generative AI relies on finding reverse models for linear discrete time forward diffusions with non-Gaussian initial states, but uses indirect methods for reversal as there is no theory for direct reversal in discrete time. We give sufficient conditions that guarantee the existence of a reverse time diffusion and give a method of meeting them. We also give a necessary and sufficient condition for the reverse model to be input-affine.",

author = "Soura Dasgupta and Anderson, \{Brian D. O.\}",

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AB - Generative AI relies on finding reverse models for linear discrete time forward diffusions with non-Gaussian initial states, but uses indirect methods for reversal as there is no theory for direct reversal in discrete time. We give sufficient conditions that guarantee the existence of a reverse time diffusion and give a method of meeting them. We also give a necessary and sufficient condition for the reverse model to be input-affine.

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BT - Proceedings of 64th IEEE Conference on Decision and Control

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ER -

Reverse-time diffusion processes in discrete time

Abstract

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