Certified L∞-Bounded Compression for AI Models, III: Compressing the Model and the Trajectory: a Tau-Collocation ODE Solver for Compressed Diffusion and Video Models

A diffusion or video generator is a large network called many times along an ordinary differentialequation. This paper compresses both. The model is compressed under the certified L∞ contractof Parts I and II: the transformers, text encoders, convolutional decoders and a UNet are storedas virtual-band indices, Qwen-Image from 54.2 to 30.3 GiB at the per-call cost of the densemodel, and MiniMax-H3 from 129 to 54 GiB (its transformer from 61 to 24 GiB at τ = 10−2,chosen from the scale of its weights). The trajectory is compressed by the same mathematicsthat compressed the weights in τ -Comp [1]: the network’s prediction D along the sampling pathis a curve, and we approximate it by a degree-1 piecewise polynomial within an error ε, with thepieces found by the split and greedy-merge calibration of τ -Comp [1]. These are two separableideas: the calibration decides where to call the network, and so how many times, and the step-by-step Tau-Collocation Method decides how to integrate between the calls; we measure eachalone and together. The nodes of the pieces are the network calls, so the number of calls is thecompressed size of the trajectory, and the step-by-step Tau-Collocation Method integrates theODE exactly on each piece. The compressed model is then evaluated at only these nodes, andan attention that reads the qvb8 indices of the keys and values lowers the cost of each call forlong video sequences. Against the model’s own default pipeline, text-to-video generation takes13 calls instead of 49 or 50 and MiniMax-H3 text-to-video takes 800 s instead of 2681 s (3.35×)with the three parts together, all measured on a single NVIDIA DGX Spark.