Optical Physics-Based Generative Models

TL;DR

This paper introduces a mathematical framework linking optical physics equations to generative models, demonstrating how nonlinear optical dynamics can improve AI generative processes with enhanced efficiency, stability, and controllability.

Contribution

It presents novel nonlinear optical models that inspire more efficient and stable generative AI methods, with significant parameter reduction and improved performance over linear models.

Findings

Nonlinear Helmholtz model reduces parameters by 40-60% while maintaining mode separation.

Cubic-quintic dissipative wave model prevents mode collapse, enabling stable solitons.

Intensity-dependent Eikonal model enhances controllability in content-driven generation.

Abstract

This paper establishes a comprehensive mathematical framework connecting optical physics equations to generative models, demonstrating how light propagation dynamics inspire powerful artificial intelligence approaches. We analyze six fundamental optical equations, comparing linear models (Helmholtz, dissipative wave, and Eikonal equations) with their nonlinear extensions incorporating Kerr effects, cubic-quintic nonlinearities, and intensity-dependent refractive indices. Our nonlinear optical models reveal remarkable capabilities through natural self-organization principles. The nonlinear Helmholtz model achieves 40-60% parameter reduction while maintaining superior mode separation via self-focusing phenomena. The cubic-quintic dissipative wave model prevents mode collapse through balanced attractive-repulsive interactions, enabling stable soliton formation with 20-40% improved coverage. The intensity-dependent Eikonal model creates adaptive pathways that dynamically respond to content, providing enhanced controllability in conditional generation. Experimental validation demonstrates consistent superiority over linear predecessors and traditional generative approaches. The nonlinear Helmholtz model achieves FID scores of 0.0089 versus 1.0909 for linear versions, while the cubic-quintic model reaches 0.0156 FID with exceptional stability. Memory usage drops 40-60% and training time improves 30-50% due to inherent nonlinear stability properties. The framework enables bidirectional benefits, advancing both generative AI and optical physics through novel approaches to soliton analysis, wavefront control, and refractive index reconstruction with 95% accuracy. This work reveals deep connections between physical self-organization and artificial intelligence, opening pathways toward efficient optical computing implementations.