# Tracing Generated Samples to Training-Data Clusters in Flow-Matching Models

arXiv: https://arxiv.org/abs/2608.30081 · HTML: https://mlsanity.com/paper/2608.30081/

## Key facts

- No citing papers in the map yet (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 16 references that are in the map.
- First posted on arXiv 30 Aug 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)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Intriguing Properties of Data Attribution on Diffusion Models](https://mlsanity.com/paper/2311.00500/) (2023)
- [The Journey, Not the Destination: How Data Guides Diffusion Models](https://mlsanity.com/paper/2312.06205/) (2023)
- [Influence Functions for Scalable Data Attribution in Diffusion Models](https://mlsanity.com/paper/2410.13850/) (2024)
- [How Do Flow Matching Models Memorize and Generalize in Sample Data Subspaces?](https://mlsanity.com/paper/2410.23594/) (2024)
- [Data Attribution for Diffusion Models: Timestep-induced Bias in Influence Estimation](https://mlsanity.com/paper/2401.09031/) (2024)
- [Nonparametric Data Attribution for Diffusion Models](https://mlsanity.com/paper/2510.14269/) (2025)
- [Exploring and Exploiting Stability in Latent Flow Matching](https://mlsanity.com/paper/2605.08398/) (2026)

## Abstract (arXiv)

Understanding which training samples influence a generated image is an important problem in generative modeling. In flow matching, training samples influence the generated image through the velocity field along the generation trajectory. Removing samples to examine their counterfactual influence changes the velocity field, and the resulting effect on the final image depends on how the change propagates through the trajectory. Consequently, local changes in the velocity field do not necessarily predict the final counterfactual effect. This work investigates attribution in flow-matching models through a hybrid analytical--learned approach, and uses it to derive trajectory-based attribution scores at the cluster level. We evaluate these attribution scores using independently retrained leave-one-cluster-out (LOCO) models, and compare with several attribution baselines using two different flow-matching latent spaces. Our experiments show that semantic similarity constitutes a strong baseline, while the closed-form trajectory-based attribution is competitive in some metrics without requiring counterfactual retraining or model gradients. Our results show that attribution in flow matching depends not only on semantic similarity to training samples, but also on the latent representation, trajectory dynamics, and how influence is propagated to the final output.