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A.1 Algorithm for Learning Categorical Data The over all training algorithm for learning categorical generative models is similar to the other cases. A.2 Practical Algorithm We give a detailed practical algorithm. N(0,I) is a standard Gaussian noise. A simplified loss Similar to Song and Ermon [41], Ho et al. [18], we use a stochastic version of loss (15), in which we only uniformly sample temporal snapshots to compute the loss. Apply gradient descent to update .