Reconstructing dynamic assets from video data is central to many in computer vision and graphics tasks. Existing 4D reconstruction approaches are limited by category-specific models or slow optimization-based methods. Inspired by the recent Large Reconstruction Model (LRM) [15], we present the Large Interpolation Model (LIM), a transformer-based feed-forward solution, guided by a novel causal consistency loss, for interpolating implicit 3D representations across time. Given implicit 3D representations at times t0and t1, LIM produces a deformed shape at any continuous time t ∈ [t0,t1] delivering high-quality interpolations in seconds (per frame). Furthermore, LIM allows explicit mesh tracking across time, producing a consistently uv-textured mesh sequence ready for integration into existing production pipelines. We also use LIM, in conjunction with a diffusion-based multi-view generator, to produce dynamic 4D reconstructions from monocular videos. We evaluate LIM on various dynamic datasets, benchmarking against image-space interpolation methods (e.g., FiLM [41]) and direct triplane linear interpolation, and demonstrate clear advantages. In summary, LIM is the first feed-forward model capable of high-speed tracked 4D asset reconstruction across diverse categories.