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

Generating long-horizon molecular dynamics (MD) is difficult due to error accumulation in time-domain autoregressive models, which causes 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 window-wise spectral representations, and a generator combines low-to-high frequency autoregression with diffusion denoising to reconstruct continuous motion. This formulation is motivated by a local near-equilibrium view of protein dynamics: after per-window alignment, fluctuations around an anchor conformation are better characterized in spectral space, where local mode structure is more explicit than in frame-wise coordinates. To improve cross-residue and cross-frequency consistency, we introduce Inter-Residue Frequency Coupling (IRFC), a learnable Gaussian distance bias in attention that injects a resonance-inspired structural prior. 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% versus MDGEN and 57.2% versus ProAR, while achieving 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 $W_2=1.19$, improving over the next best method by 50.03%, 35.25%, and 47.58%, respectively. It also improves near-equilibrium local-dynamics and covariance consistency, achieving PCA-PSD-LogCorr $=0.817$ and CFRE $=0.989$, corresponding to a 21.9% gain and a 36.7% reduction over the next best method, respectively. The source code is available at https://github.com/Linmj-Judy/BioDynaSpec.git.