Trajectory inference via Acceleration Matching
Bartolo Dazzini, Giovanni Conforti, Alain Durmus, Aram-Alexandre Pooladian
cs.LG, math.OC, stat.ML
Submitted: 2026-08-04
Comments: Comments welcome!
License: http://creativecommons.org/licenses/by/4.0/
The gist: Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories
Terminology
Abstract
Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data. Existing algorithms exhibit computational challenges: they either rely on preprocessing subroutines to enforce smoothness or on simulation-based training objectives, both of which can be expensive. In order to overcome these limitations, we propose a new algorithm called Acceleration Matching (AM). Our approach consists of lifting the original interpolation problem to phase space and then regressing onto an explicit conditional acceleration field that induces random, smooth trajectories that agree with the prescribed marginals. Importantly, our resulting training algorithm only requires positional data, avoids trajectory simulation during training, and is devoid of expensive preprocessing. We provide ample numerical evidence suggesting that AM is competitive with or superior to existing algorithms on several benchmark problems from the existing literature.
Sources
- Stochastic interpolants with data-dependent couplings
- Building Normalizing Flows with Stochastic Interpolants
- Flow Matching on General Geometries
- Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
- Flow Matching for Generative Modeling
- Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
- Entropic estimation of optimal transport maps
- Multi-marginal Schr\"odinger Bridges with Iterative Reference Refinement
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