IIHS: Innovation-Insulated Heat Splats for Single-Image Representation Learning

Neural fields have become a dominant representation-learning paradigm: coordinate networks store an image in the weights of a continuous function, and Gaussian splatting uses explicit primitives that are fast to render and compact to store. Structural priors steer where these primitives are placed, but each primitive's footprint remains blind to image structure: an anisotropic Gaussian elongated along an edge still bleeds across it. We present Innovation-Insulated Heat Splats (IIHS), a single-image representation in which each source starts as a small Gaussian and spreads as heat through a medium that insulates at the innovations of the image, i.e., the discontinuities where it changes abruptly, so that its heat is held back at the boundary of its region. The decoder derives this medium from its own free-space render, so it costs no bits. Because the medium only needs the innovations, the same representation extends to degraded observations, where we read them with the annihilating-filter subspace of finite-rate-of-innovation sampling instead of the image gradient. At equal stored rate, IIHS is around $2$ dB above the Gaussian-splat representations at low rates on Kodak-24 and DIV2K. When fitted to super-resolution and inpainting, it improves over them with the lowest LPIPS of all methods. Broadly, our work suggests that where a representation stops can matter as much as what it stores.