Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or highly expressive iterative samplers (e.g., Diffusion and Energy-based Models), which are costly and opaque. We introduce the Kolmogorov-Arnold Energy Model (KAEM) to bridge this trade-off and provide new opportunities for latent-space interpretability. Based on a novel adaptation of the Kolmogorov-Arnold Representation Theorem, KAEM imposes a univariate latent structure on the prior, enabling exact inference via the inverse transform method. With a low-dimensional latent space and appropriate inductive biases, importance sampling becomes a tractable, unbiased, and efficient posterior inference method. For settings where this fails, we propose a population-based strategy that decomposes the posterior into a sequence of annealed distributions, a new remedy for poor mixing in Energy-based Models. We compare KAEM against VAEs, the neural latent EBM architecture, and a denoising diffusion probabilistic model. Across SVHN, CIFAR10, and CelebA, KAEM attains the best Fréchet Inception Distance among latent-prior models, while sampling in a single forward pass and exposing an interpretable prior built from 1D densities.

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