HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps

2026-09-26

AI Summary

This study addresses the challenge of predicting smooth dynamics with collisions, which requires jointly modeling continuous evolution and abrupt state transitions—a task where existing methods struggle to balance accuracy with long-term stability. We propose a dual-expert diffusion field framework that unifies both dynamic regimes by integrating full-window denoising with Hamiltonian propagation. To ensure geometric fidelity and computational efficiency, affine symplectic mappings are incorporated into the solver. Furthermore, hybrid state feedback is introduced to suppress autoregressive error accumulation, while parallel local affine scans combined with regime-model trees balance typical and tail errors. Evaluated on benchmark datasets, our approach reduces phase-space mean squared error by over 20% and achieves state-of-the-art long-horizon position and momentum errors, significantly outperforming existing baselines.

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/.

Problem

• dynamics prediction
• collision modeling
• Hamiltonian systems
• error accumulation
• phase-space prediction

Innovation

• Dual-Expert Diffusion Fields
• Hamiltonian Propagation
• Parallel Local Affine Scan
• Affine Symplectic Maps
• Regime Model Tree