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In this comment on "Solving Statistical Mechanics Using VariationalAutoregressive Networks" by Wu et al., we propose a subtle yet powerfulmodification of their approach. We show that the inherent sampling error oftheir method can be corrected by using neural network-based MCMC or importancesampling which leads to asymptotically unbiased estimators for physicalquantities. This modification is possible due to a singular property of VANs,namely that they provide the exact sample probability. With thesemodifications, we believe that their method could have a substantially greaterimpact on various important fields of physics, including strongly-interactingfield theories and statistical physics.

Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Sampling