Learning Implicit Bias in Generative Spaces for Accelerating Protein Dynamics Emulation

Protein dynamics underlie many biological functions, yet remain difficult to characterize due to the high computational cost of molecular dynamics simulations and the scarcity of dynamic structural data. This survey reviews recent advances in artificial intelligence for protein dynamics from three perspectives: learning from structural ensembles and trajectories, learning from physical energy signals, and learning to accelerate molecular simulations. We summarize representative methods for conformation ensemble generation, trajectory generation, Boltzmann generators, physics-aware adaptation, machine learning potentials, coarse-grained modeling, and collective variable discovery. We further discuss available datasets and key open challenges, such as scalability, thermodynamic consistency, kinetic fidelity, and integration with experimental constraints.

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that generate independent samples from complex molecular distributions, eliminating the cost of sampling rare transition events. However, a sampling problem remains when computing observables that rely on states which are rare in equilibrium, for example folding free energies. Here, we introduce enhanced diffusion sampling, enabling efficient exploration of rare-event regions while preserving unbiased thermodynamic estimators. The key idea is to perform quantitatively accurate steering protocols to generate biased ensembles and subsequently recover equilibrium statistics via exact reweighting. We instantiate our framework in three algorithms: UmbrellaDiff (umbrella sampling with diffusion models), MetaDiff (a batchwise analogue for metadynamics), and $Δ$G-Diff (free-energy differences via tilted ensembles). Across toy systems, protein folding landscapes and folding free energies, our methods achieve fast, accurate, and scalable estimation of equilibrium properties within GPU-minutes to hours per system-closing the rare-event sampling gap that remained after the advent of diffusion-model equilibrium samplers.

Computational enzyme design requires generating proteins that scaffold catalytic residues and ligands, a task that demands both geometric accuracy and structural diversity from the underlying generative model. Current all-atom generators inherit expensive architectures from structure prediction, leading to high training costs and limited sample diversity. We argue that much of this complexity is unnecessary for generators, which condition on sparse geometric constraints rather than rich co-evolutionary signals. Emyx is a 140M-parameter conditional flow matching model that concentrates capacity within standard transformer blocks, replacing heavy embedding stacks with lightweight conditional representations and sparse connectivity. We additionally derive an exact reparametrisation of the flow matching interpolant into the EDM noise-level framework, bridging flow matching training efficiency with state-of-the-art sampling methods designed for diffusion models without retraining. Despite being the smallest model, Emyx outperforms both Proteína-Complexa and RFdiffusion3 against the AME enzyme design benchmark across success rate under strict evaluation requiring both global fold recovery and catalytic geometry accuracy, structural novelty, scaffold diversity, and geometric validity, while training in just $682$ GPU-hours, roughly $4\times$ less than RFdiffusion3.