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

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 “learning the proper initial noise.” Given an observation, VFM learns a noise adapter that outputs a noise distribution whose samples are mapped to data space by a flow map, respecting both the observation and the data prior. A principled variational objective jointly trains the adapter and flow map to improve noise-data alignment. Across image inverse problems, VFM produces well-calibrated conditional samples in one or a few steps; on ImageNet, it achieves competitive fidelity while sampling orders of magnitude faster than iterative diffusion and flow baselines.