用光学物理方程构建生成模型，实现更高效稳定的图像生成。
Optical Physics-Based Generative Models
- 将非线性光学方程融入生成模型，利用自聚焦等物理机制提升性能。
- 非线性赫尔姆霍兹模型参数减少40%-60%，FID降至0.0089，显著优于线性模型。
- 适合关注物理启发式AI、低资源生成模型或光学计算的科研人员。
本文建立了一个连接光学物理方程与生成模型的综合数学框架，揭示光传播动力学如何启发强大的人工智能方法。分析了六种基础光学方程，比较线性模型（亥姆霍兹、耗散波、费金方程）与其非线性扩展（含克尔效应、立方-五次非线性、强度依赖折射率）。非线性模型通过自然自组织机制展现卓越能力：非线性亥姆霍兹模型实现40%-60%参数压缩，保持优异模式分离；立方-五次耗散波模型通过吸引-排斥平衡防止模式坍缩，实现稳定孤子生成，覆盖度提升20%-40%；强度依赖费金模型生成动态响应内容的自适应路径，增强条件生成可控性。实验验证表明，非线性亥姆霍兹模型FID达0.0089，远优于线性版本的1.0909；立方-五次模型FID为0.0156，具备极佳稳定性。内存占用降低40%-60%，训练时间提速30%-50%。该框架双向赋能：推动生成AI与光学物理发展，实现孤子分析、波前控制与折射率重构95%准确率。揭示了物理自组织与人工智能的深层关联，为高效光学计算提供新路径。
原文摘要 · Abstract (English)
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.
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