Conditional Stochastic Interpolation for Generative Learning
This work addresses conditional distribution learning for generative modeling, presenting an incremental improvement with adaptive diffusion to handle instability.
The authors tackled the problem of learning conditional distributions by proposing a conditional stochastic interpolation (CSI) method, which estimates probability flow equations to transport a reference distribution to the target, resulting in nonasymptotic error bounds and application to image generation on a benchmark dataset.
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.