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This paper studies the problem of learning the conditional distribution of ahigh-dimensional output given an input, where the output and input may belongto two different domains, e.g., the output is a photo image and the input is asketch image. We solve this problem by cooperative training of a fast thinkinginitializer and slow thinking solver. The initializer generates the outputdirectly by a non-linear transformation of the input as well as a noise vectorthat accounts for latent variability in the output. The slow thinking solverlearns an objective function in the form of a conditional energy function, sothat the output can be generated by optimizing the objective function, or morerigorously by sampling from the conditional energy-based model. We propose tolearn the two models jointly, where the fast thinking initializer serves toinitialize the sampling of the slow thinking solver, and the solver refines theinitial output by an iterative algorithm. The solver learns from the differencebetween the refined output and the observed output, while the initializerlearns from how the solver refines its initial output. We demonstrate theeffectiveness of the proposed method on various conditional learning tasks,e.g., class-to-image generation, image-to-image translation, and imagerecovery. The advantage of our method over GAN-based methods is that our methodis equipped with a slow thinking process that refines the solution guided by alearned objective function.

Cooperative Training of Fast Thinking Initializer and Slow Thinking Solver for Conditional Learning