What question did this study set out to answer?

The aim is to develop a framework that integrates prior knowledge into generative diffusion models, enhancing their applicability in scientific and engineering domains.

May 27, 2026Open Access

Prior-Guided Diffusion Processes: A Unified Framework for Knowledge-Informed Generative Modeling with Theoretical Guarantees and Prognostic Case Studies

Puntos clave

The aim is to develop a framework that integrates prior knowledge into generative diffusion models, enhancing their applicability in scientific and engineering domains.
Introduced Prior-Guided Diffusion Processes (PGDP) to augment score functions with domain knowledge.
Analyzed guided path measures and established theoretical upper bounds on Kullback–Leibler divergence.
Conducted experiments on synthetic data and applied PGDP to the NASA C-MAPSS turbofan benchmark.
Confirmed dependence on guidance strength γt through experiments on synthetic data.
Achieved a 99.98% reduction in monotonicity loss on the NASA IGBT accelerated aging dataset.
Demonstrated generality of PGDP across distinct degradation mechanisms while enforcing physical constraints.

Resumen

Diffusion probabilistic models are powerful generative tools but are purely data-driven, limiting their ability to incorporate domain knowledge—such as physical laws, degradation trends, or engineering priors—in scientific and engineering applications. We introduce Prior-Guided Diffusion Processes (PGDPs), a unified mathematical framework that integrates arbitrary differentiable prior knowledge into the reverse diffusion dynamics by augmenting the score function with a guidance term derived from a prior potential V(x,t) and weighted by a time-dependent strength γt. This formulation subsumes existing mechanisms (classifier guidance, model-based diffusion, physics-informed corrections) as special cases. We analyze the guided path measures, providing an upper bound on the Kullback–Leibler divergence between guided and unguided marginals (Theorem 1), quantifying the inherent trade-off between data fidelity and prior satisfaction. Experiments on synthetic data confirm the predicted dependence on γt. On the NASA C-MAPSS turbofan benchmark, we enforce compressor-oriented physical constraints (e.g., speed–pressure consistency, monotonicity) within PGDP; remaining useful life scores are reported only as reference metrics under transparent protocols. A cross-domain study on the NASA IGBT accelerated aging dataset, using the same backbone with a replaced physics module, achieves a 99.98% reduction in monotonicity loss, demonstrating generality across distinct degradation mechanisms. PGDP provides a principled, extensible template for knowledge-informed generative modeling with theoretical guarantees and verifiable physical consistency.

Leer artículo completoexternamente

Me gusta

Guardar

Ver artículo completo