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

Generating long-horizon, all-atom 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 $R_{250}=1.509$ Å (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.