# NullFlow: One-Step Generative Reconstruction

arXiv: https://arxiv.org/abs/2606.22696 · HTML: https://mlsanity.com/paper/2606.22696/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 33 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2503.08136/) (2025)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [One-step Latent-free Image Generation with Pixel Mean Flows](https://mlsanity.com/paper/2601.22158/) (2026)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [Flower: A Flow-Matching Solver for Inverse Problems](https://mlsanity.com/paper/2509.26287/) (2025)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)

## Built on by (most cited first, 2 of 2)

- [Consistency Models for Fast MRI Reconstruction Using Regularization by Denoising](https://mlsanity.com/paper/2608.20561/) (2026)
- [SNaP: One-Step Posterior Sampling for Noisy Inverse Problems](https://mlsanity.com/paper/2609.34071/) (2026)

## Abstract (arXiv)

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.