Variational Flow Maps: Make Some Noise for One-Step Conditional Generation

摘要

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and solving inverse problems. We put forth _Variational Flow Maps_, a framework for conditional sampling that shifts the perspective of conditioning from "guiding a sampling path", to that of "learning the proper initial noise". Specifically, given an observation, we seek to learn a _noise adapter model_ that outputs a noise distribution, so that after mapping to the data space via flow map, the samples respect the observation and data prior. To this end, we develop a principled variational objective that jointly trains the noise adapter and the flow map, improving noise-data alignment, such that sampling from complex data posterior is achieved with a simple adapter. Experiments on various inverse problems show that VFMs produce well-calibrated conditional samples in a single (or few) steps. For ImageNet, VFM attains competitive fidelity while accelerating the sampling by orders of magnitude compared to alternative iterative diffusion/flow models.