Neural Diffusion Processes for Physically Interpretable Survival Prediction

Survival analysis is central in many applications across medicine, engineering, economics and finance. It concerns time-to-event modeling: given a process that can generate an event of interest (e.g., death from disease, failure due to wear), the goal is to estimate the probability that an event occurs at any time t > 0 for an individual described by some input variables (or features, or covariates). Unlike standard regression settings, survival data are characterized by censoring, which means that for some instances, the exact event time is not observed (for example, when individuals remain event-free at the end of the study), and only the last recorded follow-up time is available. Traditional approaches to survival modeling rely on strong statistical assumptions linking input variables and risk. The Cox proportional hazards (CoxPH) model [1] remains the most widely used and best established method. The proportional hazards assumption implies that the instantaneous risk of event for two individuals differs by a constant factor over time. The CoxPH model is also linear, making it clear how each single input variable affects the outcome, but at the expense of missing interactions between features. In its original form, this relation is modeled through a linear regression on the features, though many extensions have been developed to relax linearity and improve performance in high-dimensional settings [2-4]. Despite its success, Cox regression is limited by the proportional hazards (PH) assumption, which is often unrealistic.