The paper introduces a novel approach to image matching based on the concept of diffusing models, inspired by Maxwell's demons. The idea is to treat image boundaries as semi-permeable membranes, allowing one image to diffuse through these interfaces by the action of effectors (demons) within the membranes. This concept is contrasted with traditional attraction-based methods, which rely on distance. Diffusing models use polarity (inside–outside) rather than distance, but can be combined with attraction through optical flow techniques. The paper presents three non-rigid matching algorithms: one using all intensity levels, one using contour points, and one using already segmented images. Experimental results are shown with synthesized and real medical images, including applications to heart motion tracking and 3D inter-patient matching. The paper also discusses related works, including optical flow methods and deformable models. It highlights the use of demons in image processing, where demons act as effectors to push or pull the model image based on polarity. The paper also addresses the bijectivity of 3D deformations and presents experimental results on 2D and 3D image sequences, including cardiac motion analysis and inter-patient matching. The results demonstrate the effectiveness of diffusing models in non-rigid matching, particularly in medical imaging applications.The paper introduces a novel approach to image matching based on the concept of diffusing models, inspired by Maxwell's demons. The idea is to treat image boundaries as semi-permeable membranes, allowing one image to diffuse through these interfaces by the action of effectors (demons) within the membranes. This concept is contrasted with traditional attraction-based methods, which rely on distance. Diffusing models use polarity (inside–outside) rather than distance, but can be combined with attraction through optical flow techniques. The paper presents three non-rigid matching algorithms: one using all intensity levels, one using contour points, and one using already segmented images. Experimental results are shown with synthesized and real medical images, including applications to heart motion tracking and 3D inter-patient matching. The paper also discusses related works, including optical flow methods and deformable models. It highlights the use of demons in image processing, where demons act as effectors to push or pull the model image based on polarity. The paper also addresses the bijectivity of 3D deformations and presents experimental results on 2D and 3D image sequences, including cardiac motion analysis and inter-patient matching. The results demonstrate the effectiveness of diffusing models in non-rigid matching, particularly in medical imaging applications.