🤖 AI Summary
This work addresses weak interpolation controllability and training instability in conditional generation. We propose Conditional Stochastic Interpolation (CSI), a framework that enables differentiable and controllable transport from a reference distribution to a target conditional distribution by modeling conditional probability flows or stochastic differential equations (SDEs). Key contributions include: (i) the first explicit formulation of the conditional drift and score function as conditional expectations; (ii) an adaptive diffusion term that enhances training stability; (iii) a non-asymptotic error bound guaranteeing convergence and generalization; and (iv) support for parameter-free regression estimation, deterministic ODE sampling, and adaptive-diffusion sampling. Extensive experiments on standard image datasets demonstrate high-quality, high-fidelity conditional generation. The method combines theoretical rigor—grounded in conditional probability flow theory—with practical effectiveness, offering improved controllability, stability, and flexibility over existing approaches.
📝 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.