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

TL;DR

Variational Flow Maps introduce a novel framework for conditional image generation that learns to produce proper initial noise, enabling high-quality, fast, and well-calibrated conditional sampling in a single or few steps.

Contribution

The paper proposes Variational Flow Maps, a new approach that shifts conditioning to learning initial noise, allowing efficient and accurate conditional sampling with flow models.

Findings

Achieves competitive image fidelity on ImageNet.

Produces well-calibrated conditional samples in few steps.

Accelerates sampling significantly compared to diffusion models.

Abstract

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. Code is available at https://github.com/abbasmammadov/VFM