molecular simulation teams

Abstract: Real data are often arbitrary, indirect observations of an unknown underlying process, and those observations can distort its geometry. Existing geometric methods equip data with the induced geometry of the ambient space, but this entangles the true geometry of the process with the distortion of the observation. To address this, we introduce Intrinsic Geometry Matching (IGM): a scalable approach to learn the intrinsic geometry of the underlying process. Specifically, we learn the carré du champ operator of the process, allowing us to recover its diffusion geometry. Our method uses the fact that data often come with natural perturbations, like steps in a time series, to recover the intrinsic carré du champ while transforming naturally with changes in observation: it is observation-equivariant. Furthermore, since this equivariance relates the geometry of different spaces, we can train a model using additional sources of data, even when that data lies in another space. We evaluate IGM on molecular dynamics, image, and video data and find better performance and scaling than existing neural and graph-based geometric tools.

Abstract: Inference-time scaling adapts pretrained diffusion models to new sampling tasks without additional training. Existing methods rely primarily on Monte Carlo sampling with more particles, yet are premised on the pretrained model being exact. In practice, data and training limitations make the model imperfect, and these methods inherit its error. More particles reduce Monte Carlo error but cannot remove the mismatch between the endpoint and the desired target or the error in tracking the prescribed probability path. We introduce the Energy-based Feynman-Kac Corrector (EBFKC), a framework for energy-based diffusion models that corrects these errors on the fly given a reference energy. We first derive Feynman-Kac dynamics that track a prescribed path exactly in the continuous-time population limit even when the model is imperfect, and approximate these dynamics using sequential Monte Carlo with variance-controlling guidance. To remove the endpoint mismatch, we use the pretrained energy as a surrogate along the diffusion path and progressively incorporate the discrepancy between the learned and target terminal energies. Experiments on Gaussian mixture models, particle systems, alanine dipeptide, and alanine tetrapeptide show that our method closely matches target distributions and molecular free-energy profiles under annealing and reward tilting, whereas standard inference-time scaling baselines retain substantial sampling errors.