Neural Diffusion Processes for Physically Interpretable Survival Prediction

We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion process to an absorbing boundary. A neural network maps input variables to physically meaningful parameters including initial condition, drift, and diffusion, within a chosen FHT process such as Brownian motion, both with drift and driftless. This yields closed-form survival and hazard functions and captures time-varying risk without assuming proportional-hazards.