Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps

Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the density of the generated samples. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson’s trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While {F2D2} uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to $10\times$ inference speedup over the fastest baseline.