This paper gives a scalable variant of score matching for partition-function-free fitting of probabilistic models: the model is written as an autoregressive conditioning chain and score matching is applied separately to each factor in the chain. All four reviewers recommend acceptance. There is a consensus that the proposed approach is novel, theoretically well-motivated, empirically well-validated, and of broad interest. Initially, several reviewers voiced concerns and questions about the empirical evaluations. The author response addressed most of these and the reviewers raised their scores accordingly. Given this the AC recommends acceptance, but strongly encourages the authors to incorporate all of the reviewer feedback in the camera ready version.