# Shortest-Path Flow Matching with Mixture-Conditioned Bases for OOD Generalization to Unseen Conditions

arXiv: https://arxiv.org/abs/2601.11827 · HTML: https://mlsanity.com/paper/2601.11827/

## Key facts

- Cited by 1 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 16 of its 41 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## 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, 16 of 16)

- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Predicting Cellular Responses to Novel Drug Perturbations at a Single-Cell Resolution](https://mlsanity.com/paper/2204.13545/) (2022)
- [Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold](https://mlsanity.com/paper/2408.14608/) (2024)
- [Modelling Cellular Perturbations with the Sparse Additive Mechanism Shift Variational Autoencoder](https://mlsanity.com/paper/2311.02794/) (2023)
- [CellFlux: Simulating Cellular Morphology Changes via Flow Matching](https://mlsanity.com/paper/2502.09775/) (2025)
- [Gaussian Mixture Flow Matching Models](https://mlsanity.com/paper/2504.05304/) (2025)
- [Carr'e du champ flow matching: better quality-generalisation tradeoff in generative models](https://mlsanity.com/paper/2510.05930/) (2025)
- [Estimation and inference for the Wasserstein distance between mixing measures in topic models](https://mlsanity.com/paper/2206.12768/) (2022)
- [MolSnap: Snap-Fast Molecular Generation with Latent Variational Mean Flow](https://mlsanity.com/paper/2508.05411/) (2025)

## Built on by (most cited first, 1 of 1)

- [DeMixPert: Decomposed Response Modeling with Gaussian Mixtures for OOD Single-Cell Perturbation Prediction](https://mlsanity.com/paper/2608.23114/) (2026)

## Abstract (arXiv)

Robust generalization under distribution shift remains a key challenge for conditional generative modeling: conditional flow-based methods often fit the training conditions well but fail to extrapolate to unseen ones. We introduce SP-FM, a shortest-path flow-matching framework that improves out-of-distribution (OOD) generalization by conditioning both the base distribution and the flow field on the condition. Specifically, SP-FM learns a condition-dependent base distribution parameterized as a flexible, learnable mixture, together with a condition-dependent vector field trained via shortest-path flow matching. Conditioning the base allows the model to adapt its starting distribution across conditions, enabling smooth interpolation and more reliable extrapolation beyond the observed training range. We provide theoretical insights into the resulting conditional transport and show how mixture-conditioned bases enhance robustness under shift. Empirically, SP-FM is effective across heterogeneous domains, including predicting responses to unseen perturbations in single-cell transcriptomics and modeling treatment effects in high-content microscopy--based drug screening. Overall, SP-FM provides a simple yet effective plug-in strategy for improving conditional generative modeling and OOD generalization across diverse domains.