We propose a two-ambient-space continuum reformulation of the Image Joint-Embedding Predictive Architecture (I-JEPA). In the standard architectural description, I-JEPA operates on discrete image patches arranged on a finite grid and predicts masked target representations in latent space. This paper makes explicit the geometric structure implicit in that process. A RGB patch is first represented as a raw patch-content vector , while its location in the image is represented by a two-dimensional patch-position vector . Together, these define a spatial-patch ambient space , in which a structured image forms an embedded graph rather than an arbitrary point cloud. After encoding, the image is lifted into a spatial-feature space , where I-JEPA performs latent prediction. On this two-ambient-space construction, we introduce a scalar visual potential , analogous to a temperature-like field, defined over the spatial-patch space. We then formulate a spatial-patch advection–diffusion equation in which variation over the patch-position space is coupled to diffusion or compatibility in the patch-content (or, after encoding, visual-feature) space. Visible context patches are interpreted as partial-observation constraints, while masked target patches are treated as unknown patch-content states to be inferred. In this view, I-JEPA’s predictor is not merely a neural module that fills missing tokens, but an approximate solution-plus-readout operator , where denotes a spatial-patch solution operator and extracts predicted vector embeddings from the scalar potential. We also discuss an elliptic or non-local alternative that better reflects the parallel self-attention structure of transformer predictors. The proposed reformulation does not claim that I-JEPA explicitly solves a known physical PDE. Rather, it provides a geometric and analytical framework for studying latent prediction, masking, compatibility, stability, and future extensions from static images to video and object-level world models.
lijia zhang (Fri,) studied this question.