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I describe a trick for training flow models using a prescribed rule as asurrogate for maximum likelihood. The utility of this trick is limited fornon-conditional models, but an extension of the approach, applied to maximumlikelihood of the joint probability distribution of data and conditioninginformation, can be used to train sophisticated \textit{conditional} flowmodels. Unlike previous approaches, this method is quite simple: it does notrequire explicit knowledge of the distribution of conditions, auxiliarynetworks or other specific architecture, or additional loss terms beyondmaximum likelihood, and it preserves the correspondence between latent and dataspaces. The resulting models have all the properties of non-conditional flowmodels, are robust to unexpected inputs, and can predict the distribution ofsolutions conditioned on a given input. They come with guarantees of predictionrepresentativeness and are a natural and powerful way to solve highly uncertainproblems. I demonstrate these properties on easily visualized toy problems,then use the method to successfully generate class-conditional images and toreconstruct highly degraded images via super-resolution.

Maximum Likelihood on the Joint (Data, Condition) Distribution for Solving Ill-Posed Problems with Conditional Flow Models