Spectral Generative Flow Models: A Physics-Inspired Replacement for Vectorized Large Language Models

Abstract

We introduce Spectral Generative Flow Models (SGFMs), a physics-inspired alternative to transformer-based large language models. Instead of representing text or video as sequences of discrete tokens processed by attention, SGFMs treat generation as the evolution of a continuous field governed by constrained stochastic dynamics in a multiscale wavelet basis. This formulation replaces global attention with local operators, spectral projections, and Navier--Stokes-like transport, yielding a generative mechanism grounded in continuity, geometry, and physical structure. Our framework provides three key innovations: (i) a field-theoretic ontology in which text and video are unified as trajectories of a stochastic partial differential equation; (ii) a wavelet-domain representation that induces sparsity, scale separation, and computational efficiency; and (iii) a constrained stochastic flow that enforces stability, coherence, and uncertainty propagation. Together, these components define a generative architecture that departs fundamentally from autoregressive modeling and diffusion-based approaches. SGFMs offer a principled path toward long-range coherence, multimodal generality, and physically structured inductive bias in next-generation generative models.