Your Model's MSE Is Lying to You III: Time Series Diffusion

A forecasting model can correctly predict the average outcome and its variance but still describe a future that is physically impossible. This failure occurs because standard models assume a single bell curve for uncertainty, which misrepresents situations with multiple distinct future paths by placing the highest probability on an intermediate state that never actually happens. Diffusion models offer a powerful solution by learning to represent complex, multi-peaked distributions that capture the true shape of potential futures. By training a network to reverse a noise-adding process, these models can generate realistic forecast samples that avoid the pitfalls of simpler statistical assumptions.