# FreeBridge: Variational Schr"odinger Bridges for Cellular Transition Dynamics

arXiv: https://arxiv.org/abs/2606.11286 · HTML: https://mlsanity.com/paper/2606.11286/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [How to Build the Virtual Cell with Artificial Intelligence: Priorities and Opportunities](https://mlsanity.com/paper/2409.11654/) (2024)
- [RxRx1: A Dataset for Evaluating Experimental Batch Correction Methods](https://mlsanity.com/paper/2301.05768/) (2023)
- [Generalized Schr"odinger Bridge Matching](https://mlsanity.com/paper/2310.02233/) (2023)
- [CellFlux: Simulating Cellular Morphology Changes via Flow Matching](https://mlsanity.com/paper/2502.09775/) (2025)
- [Ouroboros: Single-step Diffusion Models for Cycle-consistent Forward and Inverse Rendering](https://mlsanity.com/paper/2508.14461/) (2025)
- [PhenDiff: Revealing Subtle Phenotypes with Diffusion Models in Real Images](https://mlsanity.com/paper/2312.08290/) (2023)
- [Let EEG Models Learn EEG](https://mlsanity.com/paper/2605.21280/) (2026)
- [Scale Where It Matters: Training-Free Localized Scaling for Diffusion Models](https://mlsanity.com/paper/2511.19917/) (2025)

## Abstract (arXiv)

High-content imaging assays quantify cellular responses to chemical and genetic perturbations, yet continuous trajectories of individual cells are unobservable because cells are chemically fixed at acquisition. Perturbation modeling therefore reduces to inferring stochastic transport between control and treated populations observed only as separate marginals. While recent generative models achieve strong end-point alignment, boundary consistency does not determine intermediate evolution: multiple stochastic processes may connect identical marginals while traversing regions unsupported by observed single-cell morphologies. We introduce FreeBridge, a Schr"odinger Bridge formulation for single-cell transition modeling under endpoint-only supervision. FreeBridge defines atomic states as instance-segmented single-cell representations, establishing a fixed cellular manifold, and learns stochastic transport constrained within this geometry via empirical latent support regularization. Across BBBC021, RxRx1, and JUMP, FreeBridge maintains competitive or improved endpoint fidelity and mechanism-of-action retention under a unified evaluation protocol; on BBBC021, it further reduces intermediate support violations. These findings highlight the importance of geometric grounding for biologically interpretable perturbation dynamics. Project page: https://y-research-sbu.github.io/FreeBridge/.