Work

Reverse-Time Diffusion Processes for Discrete Time Linear and Nonlinear Systems with non-Gaussian Noise

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.23947

Authors: Dasgupta, Soura, Anderson, Brian D. O., Mudumbai, Raghuraman

Institutions: Australian National University, University of Iowa

Language: English

Topic: Gaussian Processes and Bayesian Inference

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7171486212

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