CMG-Inspired Causal Memory Diffusion for Artificial Intelligence

This work introduces a causal-memory diffusion layer for artificial intelligence, motivated by the network-memory structure of Causal Memory Gravity and by entropy-driven anisotropic diffusion. The model assigns each graph or image edge a non-negative dynamical memory state, converts that state into a bounded conductance, and evolves features through a conservative diffusion operator. The instantaneous-memory limit reproduces a Perona–Malik-type conductance law. For finite memory time, the diffusion gate depends on the past mismatch of connected features and may be transported with moving image structure. Positivity, mean conservation, and a discrete maximum-principle condition are established analytically and checked by 22 invariant and unit tests. The numerical study includes static synthetic denoising, controlled synthetic video, motion-transport and flow-error ablations, and photo-derived sequences with motion estimated from noisy frames. Static memory does not provide a free improvement over the instantaneous Perona–Malik baseline: it preserves boundaries slightly better while retaining more noise. In temporal data, carried memory consistently improves reconstruction, edge accuracy, and temporal stability relative to framewise diffusion. Transporting memory with motion provides an additional structural gain, while confidence gating limits damage when the estimated motion is unreliable.