Mujie Lin

Mujie Lin

M.Phil. in Computer Science @ PKU. Building AI systems for molecular discovery, protein dynamics, and scientific foundation models.

BioDynaSpec: Harmonic-Guided Spatio-Spectral Autoregressive Diffusion for Protein Dynamics Generation

Published in International Conference on Machine Learning (ICML 2026), 2026

Abstract

Generating long-horizon molecular dynamics (MD) is difficult due to error accumulation in time-domain autoregressive models (causing drift) and fixed step-size constraints on temporal resolution. We propose BioDynaSpec, which reformulates protein dynamics as spatio-spectral generation: Independent Windowed Fourier Decomposition (IWFD) decomposes trajectories into independent windowed frequency representations, and a generator combines low-to-high frequency autoregression with diffusion denoising to reconstruct continuous motion. We introduce Inter-Residue Frequency Coupling (IRFC) bias, a learnable Gaussian distance bias in attention that injects a resonance-inspired structural prior to stabilize training and improve cross-residue, cross-frequency consistency. On ATLAS, BioDynaSpec improves 250-frame trajectory generation with $R_{250}=1.509\,\text{\AA}$ (where $R_s$ denotes the mean per-frame C$\alpha$-RMSE over the first $s$ frames after alignment), reducing error by 60.4\% vs.\ MDGEN and 57.2\% vs.\ ProAR, and achieves the best PCA-2D displacement-profile correlation and stepwise distribution matching. For equilibrium conformational sampling, it achieves Root Mean $W_2=1.31$, MD PCA $W_2=0.90$, and Joint PCA $W_2=1.19$ (50.03\%, 35.25\%, and 47.58\% lower than the next best), while ablations show removing IRFC severely degrades RMSE/MAE and correlation. The source code is available at \url{https://anonymous.4open.science/r/BioDynaSpec-4F51/}.

Contribution

First author. Led end-to-end: problem formulation, method design (IWFD, hybrid AR-diffusion, IRFC), training pipeline, experiments, and manuscript writing.

Recommended citation: Mujie Lin, Yutian Liu, Yudi Guo, Yanzhen Hou, Yiheng Tao, Ruochong Zheng, Kaiwen Cheng, Xin Shan, Youdong Mao, Jie Chen. "BioDynaSpec: Harmonic-Guided Spatio-Spectral Autoregressive Diffusion for Protein Dynamics Generation." ICML, 2026.
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