MorseDistill: Spatio-Temporal Morse-Guided Distillation for Efficient Wildfire Forecasting

Wildfires have become one of the most widespread natural hazards worldwide, posing severe threats to communities and ecosystems. Recent series of devastating wildfires have further underscored a critical need for more holistic, accurate, and efficient prediction of _when and where_ new fire events may occur. Emerging generative AI tools, particularly Transformer-based diffusion models, can capture the complex spatio-temporal dependencies exhibited by wildfires, but their architectural complexity and iterative denoising make inference computationally expensive. Knowledge distillation offers a path toward more efficient models, yet standard approaches apply uniform supervision across all events and ignore their distinct structural roles. We propose _MorseDistil_, a Morse-guided knowledge distillation framework that distills a Transformer-based teacher into a lightweight MLP student. Inspired by the concepts from low-dimensional topology, our central idea is to use the latent topological structure of the event sequence to guide knowledge transfer. Specifically, we construct a graph abstraction for spatio-temporal event representation and identify critical events through discrete Morse functions and their gradient pairings. These critical events then shape the distillation loss, concentrating teacher supervision on the most essential spatial and temporal structures. Extensive experiments on 10 wildfire benchmarks demonstrate that MorseDistill achieves superior predictive performance at substantially lower computational costs. We validate MorseDistill with respect to the state-of-the-art baselines on a diverse set of wildfire datasets, demonstrating MorseDistill's superior predictive capabilities of up to 40.6% in relative gains under reduced computational costs of up to 96.2%.