Papers › Oh SnapMMD! Forecasting Stochastic Dynamics Beyond the Schrödinger Bridge's End
Oh SnapMMD! Forecasting Stochastic Dynamics Beyond the Schrödinger Bridge's End
Renato Berlinghieri, Yunyi Shen, Jialong Jiang, Tamara Broderick
Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional state measurements (snapshots) from different biological replicates at different time points, but they cannot access the trajectory of any one cell because measurement destroys the cell. Researchers want to forecast (e.g.) differentiation outcomes from early state measurements of stem cells. Recent Schr\"odinger-bridge (SB) methods are natural for interpolating between snapshots. But past SB papers have not addressed forecasting -- likely since existing methods either (1) reduce to following pre-set reference dynamics (chosen before seeing data) or (2) require the user to choose a fixed, state-independent volatility since they minimize a Kullback-Leibler divergence. Either case can lead to poor forecasting quality. In the present work, we propose a new framework, SnapMMD, that learns dynamics by directly fitting the joint distribution of both state measurements and observation time with a maximum mean discrepancy (MMD) loss. Unlike past work, our method allows us to infer unknown and state-dependent volatilities from the observed data. We show in a variety of real and synthetic experiments that our method delivers accurate forecasts. Moreover, our approach allows us to learn in the presence of incomplete state measurements and yields an R²-style statistic that diagnoses fit. We also find that our method's performance at interpolation (and general velocity-field reconstruction) is at least as good as (and often better than) state-of-the-art in almost all of our experiments.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections