HollowFlow: Efficient Sample Likelihood Evaluation using Hollow Message Passing

Flow and diffusion-based models have emerged as powerful tools for scientific applications, particularly for sampling non-normalized probability distributions, as exemplified by Boltzmann Generators (BGs). A critical challenge in deploying these models is their reliance on sample likelihood computations, which scale prohibitively with system size n, often rendering them infeasible for large-scale problems. To address this, we introduce HollowFlow, a flow-based generative model leveraging a novel non-backtracking graph neural network (NoBGNN). By enforcing a block-diagonal Jacobian structure, HollowFlow likelihoods are evaluated with a constant number of backward passes in n, yielding speed-ups of up to O(n2): a significant step towards scaling BGs to larger systems. Crucially, our framework generalizes: any equivariant GNN or attention-based architecture can be adapted into a NoBGNN.