Uploaded August 2026 | Updated September 2026, 2 weeks ago
Aram-Alexandre Pooladian (Yale University)
https://simons.berkeley.edu/talks/aram-alexandre-pooladian-yale-university-2026-08-04
Diffusion Generative Modeling: Progress and Next Steps
Given snapshot observations of a stochastic process, how can one reconstruct a smooth dynamical evolution consistent with all observed marginals? A natural object of interest is the probability spline (P-spline): a smooth path in the space of probability measures that interpolates prescribed marginals in direct analogy with classical cubic splines. Existing approaches to learning such paths are typically formulated through multi-marginal Schrödinger bridge problems or flow-matching objectives. While powerful, these methods often rely on simulation-based procedures, intricate preprocessing pipelines, or numerically delicate training objectives. In this work, we introduce **Acceleration Matching**, a new framework for learning probability splines through the estimation of a conditional acceleration field. Our approach is entirely simulation-free and is trained via a simple, explicit regression objective requiring virtually no preprocessing. Conceptually, it shifts the focus from matching velocities or transport maps to directly learning the second-order structure governing probabilistic dynamics. Across a range of benchmarks, Acceleration Matching achieves performance competitive with—and frequently superior to—state-of-the-art alternatives while substantially reducing training time. These results suggest that second-order learning principles may provide a scalable and effective foundation for interpolation and generative modeling in probability space.
Aram-Alexandre Pooladian (Yale University)
https://simons.berkeley.edu/talks/aram-alexandre-pooladian-yale-university-2026-08-04
Diffusion Generative Modeling: Progress and Next Steps
Given snapshot observations of a stochastic process, how can one reconstruct a smooth dynamical evolution consistent with all observed marginals? A natural object of interest is the probability spline (P-spline): a smooth path in the space of probability measures that interpolates prescribed marginals in direct analogy with classical cubic splines. Existing approaches to learning such paths are typically formulated through multi-marginal Schrödinger bridge problems or flow-matching objectives. While powerful, these methods often rely on simulation-based procedures, intricate preprocessing pipelines, or numerically delicate training objectives. In this work, we introduce **Acceleration Matching**, a new framework for learning probability splines through the estimation of a conditional acceleration field. Our approach is entirely simulation-free and is trained via a simple, explicit regression objective requiring virtually no preprocessing. Conceptually, it shifts the focus from matching velocities or transport maps to directly learning the second-order structure governing probabilistic dynamics. Across a range of benchmarks, Acceleration Matching achieves performance competitive with—and frequently superior to—state-of-the-art alternatives while substantially reducing training time. These results suggest that second-order learning principles may provide a scalable and effective foundation for interpolation and generative modeling in probability space.
