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arXiv · 2609.32838

HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps

Haoxiang Huang·Xiang Liu·Shuwei Wang·Jingheng Ma·Sen Cui
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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: https://hamiformer.github.io/.

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Haoxiang Huang, Xiang Liu, Shuwei Wang, Jingheng Ma, Sen Cui. 2026-09-26. HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps. https://arxiv.org/abs/2609.32838

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