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Simulation-Free Schrödinger Bridges via Score and Flow Matching
Alexander Tong · Nikolay Malkin · Kilian Fatras · Lazar Atanackovic · Yanlei Zhang · Guillaume Huguet · Guy Wolf · Yoshua Bengio

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in New Frontiers in Learning, Control, and Dynamical Systems »
Event URL: https://openreview.net/forum?id=adkj23mvB0 »
We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired source and target samples drawn from arbitrary distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger bridge (SB) problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data.

Author Information

Alexander Tong (Mila)
Nikolay Malkin (Mila / Université de Montréal)
Kilian Fatras (Mila, McGill university)

I am a PostDoctoral fellow at Mila laboratory and McGill University working with Adam Oberman and Ioannis Mitliagkas. I am working on Out-of-Distribution samples and Optimal Transport. Prior to my PostDoc, I was a PhD candidate under the supervision of Pr. Nicolas Courty and Pr. Rémi Flamary at INRIA Rennes. My research focused on optimal transport, machine learning and optimization with applications in large scale settings and noisy labels.

Lazar Atanackovic (University of Toronto Vector Institute)
Yanlei Zhang (Montreal Institute for Learning Algorithm)
Guillaume Huguet (Mila)
Guy Wolf (Université de Montréal; Mila)
Yoshua Bengio (Mila - Quebec AI Institute)

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