Theoretical Analysis of Engression and Reverse Markov Engression
2026-05-31 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study Engression, a new method for learning how to generate data based on certain conditions. They focus on understanding how well this method works using deep neural networks, providing clear mathematical guarantees for its accuracy with limited data. For a special version called Reverse Markov, they create a way to track how errors build up during the multi-step generation process. Their results show that Engression performs nearly as well as the best possible methods for a broad class of problems.
EngressionConditional distribution learningEnergy DistanceReverse Markov processDeep neural networksNonasymptotic convergenceExcess risk boundsMinimax rateHölder classGenerative modeling
Authors
Jiaqi Huang, Gongjun Xu, Ji Zhu
Abstract
Engression is a recently proposed and effective framework for conditional distribution learning. Its multi-step Reverse Markov extension further improves generative flexibility by decomposing complex conditional sampling into sequential reverse transitions. Despite their strong empirical performance, rigorous finite-sample statistical guarantees for these methods remain unavailable. In this paper, under deep neural network parameterizations, we establish nonasymptotic convergence bounds for Engression by directly controlling the Energy Distance between the learned and target conditional distributions. For the Reverse Markov framework, we further develop an Energy-Distance-based chain rule that enables a rigorous analysis of error propagation across reverse steps. Our analysis yields corresponding excess-risk bounds that are near-optimal up to logarithmic factors relative to the classical minimax rate over a general Hölder class.