Autoregressive Boltzmann Generators

Efficiently sampling molecular systems at thermodynamic equilibrium is a major challenge in statistical physics, as high-energy barriers between metastable states make traditional Molecular Dynamics (MD) computationally prohibitive. Boltzmann Generators (BGs) address this by learning a generative model to propose equilibrium samples. However, current BGs rely on normalizing flows, which face a fundamental trade-off: discrete-time flows are limited by strict invertibility constraints, while continuous-time flows require computationally expensive ODE integration. This paper asks whether an autoregressive framework can bypass these limitations.

The authors introduce Autoregressive Boltzmann Generators (ArBG), which factorize the molecular density into a sequence of conditional distributions. Unlike flow-based models, ArBG does not require invertible mappings, allowing it to model complex, multi-modal distributions without the topological constraints that typically plague normalizing flows. The authors implement this using a uniform binning strategy, where continuous atomic coordinates are discretized into bins, enabling the model to leverage architectures similar to those used in Large Language Models (LLMs). This structure also permits sequential inference-time interventions, such as Autoregressive Twisted Sequential Monte Carlo, which allows for the early rejection of physically implausible conformations.

ArBG demonstrates significant improvements over existing flow-based models across all tested benchmarks, particularly for larger systems like the 10-residue peptide Chignolin. The authors introduce ROBIN, a 132-million parameter model trained with the ArBG framework, which shows strong zero-shot generalization capabilities. Compared to the previous state-of-the-art (Prose), ROBIN reduces the zero-shot energy error (E-W2) on 8-residue systems by over 60%. The results highlight that ArBG scales effectively with model size and provides a more stable, expressive alternative to traditional flow-based Boltzmann Generators.