Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
arXiv:2410.01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures. A key ingredient is a probabilistic framework combining adjoint Feynman-Kac representations with synchronous coupling (and reflection c
The continuous research in generative AI models necessitates advancements in understanding and controlling their robustness and the preservation of data structure during generation.
Improved theoretical understanding and mathematical tools for generative models allow for more stable, reliable, and controllable AI systems, crucial for deployment in sensitive applications.
This research provides a new framework to analyze the robustness and structure preservation of flow-based generative models using a novel Wasserstein path-space divergence, enabling better design and evaluation.
- · AI researchers and developers
- · Industries relying on generative AI
- · Users of generative AI applications
- · Developers of unstable generative AI models
- · Legacy methods for robustness analysis
Enhanced reliability and interpretability of complex generative AI models become possible.
Broader adoption of generative AI in critical domains due to increased trust in model stability and predictability.
Acceleration of research into provably robust and safe AI systems, setting new standards for AI development.
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