The paper presents a novel approach to image-to-image matching using diffusing models, inspired by the concept of Maxwell's demons. The main idea is to treat the boundaries of one image as semi-permeable membranes and let the other image, considered as a deformable grid, diffuse through these interfaces. The authors illustrate this concept by analogy with Maxwell's demons, showing that it relates to more traditional methods based on attraction, with an intermediate step being optical flow techniques. They derive three different non-rigid matching algorithms from the diffusing model concept: one using all intensity levels in the static image, one using only contour points, and a last one operating on already segmented images. The paper also discusses the implementation details and presents experimental results with synthesized deformations and real medical images, including applications to heart motion tracking and three-dimensional inter-patient matching. The authors conclude that diffusing models provide a global understanding of how deformable models diffuse through scene interfaces to align points with similar polarities or types.The paper presents a novel approach to image-to-image matching using diffusing models, inspired by the concept of Maxwell's demons. The main idea is to treat the boundaries of one image as semi-permeable membranes and let the other image, considered as a deformable grid, diffuse through these interfaces. The authors illustrate this concept by analogy with Maxwell's demons, showing that it relates to more traditional methods based on attraction, with an intermediate step being optical flow techniques. They derive three different non-rigid matching algorithms from the diffusing model concept: one using all intensity levels in the static image, one using only contour points, and a last one operating on already segmented images. The paper also discusses the implementation details and presents experimental results with synthesized deformations and real medical images, including applications to heart motion tracking and three-dimensional inter-patient matching. The authors conclude that diffusing models provide a global understanding of how deformable models diffuse through scene interfaces to align points with similar polarities or types.