# A Flow Matching Framework for Neural Representational Dissimilarity

arXiv: https://arxiv.org/abs/2609.31544 · HTML: https://mlsanity.com/paper/2609.31544/

## 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 12 of its 50 references that are in the map.
- First posted on arXiv 25 Sep 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, 12 of 12)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Efficient Video Prediction via Sparsely Conditioned Flow Matching](https://mlsanity.com/paper/2211.14575/) (2022)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)

## Abstract (arXiv)

Neural representational dissimilarity quantifies differences between neural response distributions, and is essential for comparing neural codes across stimuli, brain areas, tasks, and models. Commonly used distance metrics involve different assumptions and are estimated with separate methods. Here, we show that a variety of distance metrics can be unified under a flow matching framework developed in deep generative models. That is, these distances arise as Jeffreys divergences under different velocity constraints. We find that flow matching has advantages for estimating distances involving complicated distributions and continuous variables. Furthermore, this framework enables the design of new distance metrics in a principled way. Together, flow matching provides a unified approach for understanding, estimating, and designing neural representational dissimilarity metrics.