Diffusion-Generated Latent Spaces for Continuous Amortized Active Inference Agents: A Mathematical Framework
摘要
We present a mathematical integration of latent diffusion models with active inference for continuous state and action spaces. Traditional active inference implementations rely on variational inference with parametric distributions, limiting their expressiveness in complex environments. We propose generating latent belief states through reverse diffusion processes, fundamentally altering how agents represent uncertainty about their environment (i.e. via diffusion-based posteriors). Our key contribution is a reformulation of the expected free energy (EFE) computation over diffusion-generated trajectories, providing a principled approach to action selection that naturally balances epistemic and pragmatic values. We establish the mathematical foundations connecting diffusion processes to the free energy principle and present algorithms for practical implementation.