Primal-Spectral Generative Modeling: Fast Analytical Generation via Pseudoinverse Levy Inversion

This paper transforms probability distributions into continuous spectral functions to make generative modeling more amenable to neural approximation, and provides theoretical guarantees for convergence to the true distribution. It introduces PriSpecNet together with a 1-NFE Pseudoinverse Levy Inversion solver that reformulates sampling as a fast analytical problem rather than iterative numerical integration. Experiments show strong improvements on time-series generation and forecasting benchmarks, while achieving competitive ImageNet 256x256 generation with FID 1.66 at dramatically lower computational cost.

Recommended citation: Zhiyuan Ouyang. "Primal-Spectral Generative Modeling: Fast Analytical Generation via Pseudoinverse Levy Inversion." ICML 2026.
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