Conditional Stochastic Interpolation for Generative Learning

TL;DR

This paper introduces a novel conditional stochastic interpolation (CSI) method for learning conditional distributions, combining stochastic differential equations with adaptive diffusion to improve stability and accuracy in generative modeling.

Contribution

The paper presents a new CSI framework that estimates conditional drift and score functions via nonparametric regression, with explicit formulas and error bounds, enhancing conditional generative modeling.

Findings

Effective in image generation tasks on benchmark datasets.

Addresses instability in diffusion processes with adaptive diffusion.

Provides theoretical error bounds for the learning process.

Abstract

We propose a conditional stochastic interpolation (CSI) method for learning conditional distributions. CSI is based on estimating probability flow equations or stochastic differential equations that transport a reference distribution to the target conditional distribution. This is achieved by first learning the conditional drift and score functions based on CSI, which are then used to construct a deterministic process governed by an ordinary differential equation or a diffusion process for conditional sampling. In our proposed approach, we incorporate an adaptive diffusion term to address the instability issues arising in the diffusion process. We derive explicit expressions of the conditional drift and score functions in terms of conditional expectations, which naturally lead to an nonparametric regression approach to estimating these functions. Furthermore, we establish nonasymptotic error bounds for learning the target conditional distribution. We illustrate the application of CSI on image generation using a benchmark image dataset.