NullFlow: One-Step Generative Reconstruction

2026-06-21

AI Summary

This work addresses the challenges of multi-step inference and reliance on additional data-fidelity correction in generative image reconstruction by introducing NullFlow, a novel framework that constrains the generative flow to the measurement-consistent subspace. This approach enables, for the first time, single-step posterior sampling without any explicit data-fidelity term, achieving high-quality reconstruction with only a single neural network forward pass. Through theoretical analysis, the authors demonstrate that the mean velocity of the constrained flow yields an optimal training objective, which is efficiently learned via one-step flow matching. Evaluated on image inpainting tasks, NullFlow matches or exceeds the performance of state-of-the-art diffusion model solvers while reducing inference cost from hundreds of network evaluations to just one.

Abstract

We propose NullFlow, a principled framework for one-step generative image reconstruction. Our key idea is to confine the generative flow to a measurement-consistent subspace. Because the flow never leaves this subspace, NullFlow needs no separate data-fidelity corrections, unlike existing solvers. NullFlow samples in a single network evaluation by learning the flow's average velocity, avoiding the step-by-step integration of traditional flow matching methods. We prove that the average velocity of this constrained flow yields a training objective whose global minimizer is a one-step posterior sampler. We show on image inpainting that NullFlow matches state-of-the-art diffusion solvers while cutting inference from hundreds of network evaluations to one.

Problem

• generative reconstruction
• one-step sampling
• image inpainting
• flow matching
• measurement consistency

Innovation

• one-step generation
• generative flow
• measurement-consistent subspace
• average velocity
• image reconstruction