# Inverse Flow and Consistency Models

arXiv: https://arxiv.org/abs/2502.11333 · HTML: https://mlsanity.com/paper/2502.11333/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 13 of 13)

- [ResShift: Efficient Diffusion Model for Image Super-resolution by Residual Shifting](https://mlsanity.com/paper/2307.12348/) (2023)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Dirichlet Diffusion Score Model for Biological Sequence Generation](https://mlsanity.com/paper/2305.10699/) (2023)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (2018)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data](https://mlsanity.com/paper/2404.10177/) (2024)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [Diffusion Model for Generative Image Denoising](https://mlsanity.com/paper/2302.02398/) (2023)
- [Deep Denoising For Scientific Discovery: A Case Study In Electron Microscopy](https://mlsanity.com/paper/2010.12970/) (2020)
- [Unsupervised Image Denoising with Score Function](https://mlsanity.com/paper/2304.08384/) (2023)

## Built on by (most cited first, 5 of 5)

- [FlowCast: Trajectory Forecasting for Scalable Zero-Cost Speculative Flow Matching](https://mlsanity.com/paper/2602.01329/) (2026)
- [FastFlow: Accelerating The Generative Flow Matching Models with Bandit Inference](https://mlsanity.com/paper/2602.11105/) (2026)
- [A Continuous-Time Consistency Model for 3D Point Cloud Generation](https://mlsanity.com/paper/2509.01492/) (2025)
- [Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets](https://mlsanity.com/paper/2608.00064/) (2026)
- [Contextual Flow Matching: Adaptive Step Selection in Flow Models for Efficient Visual Generation](https://mlsanity.com/paper/2610.03202/) (2026)

## Abstract (arXiv)

Inverse generation problems, such as denoising without ground truth observations, is a critical challenge in many scientific inquiries and real-world applications. While recent advances in generative models like diffusion models, conditional flow matching, and consistency models achieved impressive results by casting generation as denoising problems, they cannot be directly used for inverse generation without access to clean data. Here we introduce Inverse Flow (IF), a novel framework that enables using these generative models for inverse generation problems including denoising without ground truth. Inverse Flow can be flexibly applied to nearly any continuous noise distribution and allows complex dependencies. We propose two algorithms for learning Inverse Flows, Inverse Flow Matching (IFM) and Inverse Consistency Model (ICM). Notably, to derive the computationally efficient, simulation-free inverse consistency model objective, we generalized consistency training to any forward diffusion processes or conditional flows, which have applications beyond denoising. We demonstrate the effectiveness of IF on synthetic and real datasets, outperforming prior approaches while enabling noise distributions that previous methods cannot support. Finally, we showcase applications of our techniques to fluorescence microscopy and single-cell genomics data, highlighting IF's utility in scientific problems. Overall, this work expands the applications of powerful generative models to inversion generation problems.