HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps

Abstract:Predicting smooth dynamics and collisions requires modeling continuous evolution and abrupt state changes. We introduce HamiFormer, a dual-expert diffusion field combining whole-window denoising with residual-corrected Hamiltonian propagation. Their mixed-state feedback attenuates the direct contribution of inherited autoregressive error: each mixed state guides subsequent propagation within the jointly refined window. Parallel Local Affine Scan (PLAS) amortizes iterative refinement across rectified-flow steps and evaluates derivatives in parallel across physical time. PLAS's affine symplectic maps achieve lower solver error and runtime than sequential explicit Euler in our evaluation. A Regime Model Tree specializes residuals and routing to balance typical-state accuracy against large tail errors. Our analysis gives conditions for physically consistent refinement and warm-start tracking, and finite-window error bounds under diffusion feedback. In 192-step evaluations, HamiFormer reduces normalized phase-space MSE by 26.3% against PhysiFormer on HamiBalls-1 and 21.4% against DiT on HamiBalls-2, with comparable model capacities. Disjoint-interval comparisons show the lowest late-horizon position and momentum errors among baselines on both datasets. Project page: this https URL.

Machine Learning (cs.LG)

arXiv:2609.32838 [cs.LG]

(or arXiv:2609.32838v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32838 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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