Is Imitation All We Need for Generative Modeling? Spectral Entropy Guidance for Extrapolative Generation in Diffusion Models

Distribution matching is a central principle of generative modeling, with models typically designed to reproduce a reference distribution as faithfully as possible. This raises the broader question of whether reference matching should be the sole objective of generative modeling. We study this question through *imaginative generation*, which seeks distributions satisfying prescribed properties while remaining as close as possible to a reference distribution. We instantiate this principle using representation-aware spectral entropy, with complementary formulations based on von Neumann and order-$2$ Rényi entropies. Both define convex constraint sets and admit a common projection-based interpretation. The spectral entropy of the data distribution defines a natural boundary, which we call the Entropy Wall. Below the wall, a spectral entropy requirement can, under suitable conditions, recover variation lost by a learned generator while reducing its discrepancy to the data distribution. Beyond the wall, the data no longer satisfies the prescribed entropy level, and the framework transitions to controlled spectral extrapolation. Under a KL-divergence anchor, we characterize the optimal targets through self-consistent spectral reweighting and derive *spectral entropy guidance*, a retraining-free mechanism for score-based and diffusion models. Our numerical experiments on synthetic and image-generation benchmarks indicate that the proposed guidance method could recover lost variation and enable controlled extrapolative generation beyond the spectral diversity of the data distribution.