ICML 2025

Inverse Flow and Consistency Models
Yuchen Zhang 1 Jian Zhou 1
Abstract
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 gen-
erative models like diffusion models, conditional
flow matching, and consistency models achieved
impressive results by casting generation as de-
noising 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 includ-
ing denoising without ground truth. Inverse Flow
can be flexibly applied to nearly any continuous
noise distribution and allows complex dependen-
cies. We propose two algorithms for learning
Inverse Flows, Inverse Flow Matching (IFM) and
Inverse Consistency Model (ICM). Notably, to de-
rive the computationally efficient, simulation-free
inverse consistency model objective, we general-
ized consistency training to any forward diffusion
processes or conditional flows, which have appli-
cations 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.
1. Introduction
Recent advances in generative modeling such as diffusion
models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song
1Lyda Hill Department of Bioinformatics, University of Texas
Southwestern Medical Center, USA. Correspondence to: Jian Zhou
<jian.zhou@utsouthwestern.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025...