Preprint
Reverse-Time Diffusion Processes for Discrete Time Linear and Nonlinear Systems with non-Gaussian Noise
arXiv
arXiv
07/27/2026
DOI: 10.48550/arxiv.2607.23947
Abstract
Generative AI relies on finding reverse time models for a discrete-time forward diffusion with non-Gaussian initial state, but uses indirect approaches as there is no theory for direct reversal in discrete time. This paper develops a theory for directly finding reverse diffusions for discrete time nonlinear processes with non-Gaussian states and process noise. We also give a necessary and sufficient condition for the reverse model to be input-affine when the forward process is linear and the process noise Gaussian, and show that for a wide variety of state densities an input-affine reverse diffusion does not exist. This is among several differences between the reversal of stochastic difference equations and their continuous time counterparts.
Details
- Title: Subtitle
- Reverse-Time Diffusion Processes for Discrete Time Linear and Nonlinear Systems with non-Gaussian Noise
- Creators
- Soura Dasgupta - University of IowaBrian D. O Anderson - Australian National UniversityRaghuraman Mudumbai - University of Iowa
- Resource Type
- Preprint
- Publication Details
- arXiv
- DOI
- 10.48550/arxiv.2607.23947
- ISSN
- 2331-8422
- Publisher
- arXiv
- Language
- English
- Date posted
- 07/27/2026
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9985214916802771
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