Hadamard codebooks replace Gaussian ones: FLUX round trips drop from tens of seconds to seconds, video nears real time on one GPU

The codebook cost of training-free generative compression becomes one fast transform. Turbo-DDCM previously stored or regenerated a Gaussian codebook whose size grows with latent dimension and atom count, reaching tens of GiB at FLUX scale, so practical runs capped the codebook to stay feasible. H-DDCM matches complete-codebook fidelity at FLUX scale while keeping the runtime efficiency of the capped variant, reducing round-trip time from tens of seconds to seconds. Turbo-DDCM either stored the complete Gaussian codebook or capped it well below the latent dimension; capping restricts the set of residual directions and lowers quality at matched bitrate. On FLUX (latent dimension about 64k) over DIV2K, PSNR and FID are compared against complete-codebook Turbo-DDCM, capped-codebook Turbo-DDCM, and DiffC; on SD 2.1, H-DDCM and complete-codebook Turbo-DDCM both round-trip in seconds, against tens of seconds for DiffC and more for DDCM.

Neither encoder nor decoder holds a codebook; they share a random seed. At each step the seed generates a Rademacher diagonal matrix, which multiplies the normalized Hadamard matrix into a randomized orthonormal basis, and the fast Walsh-Hadamard transform supplies projection and reconstruction without writing the dictionary to memory. Because that basis is exactly orthogonal, thresholding the largest correlations and quantizing coefficients is the exact solution of the sparse least-squares problem, not merely an approximation valid for nearly orthogonal Gaussian atoms. Turbo-DDCM relied on the approximate orthogonality of high-dimensional Gaussian atoms to justify the same thresholding rule, and needed dense matrix products to access its codebook. Image experiments run on two backbones, SD 2.1 (latent dimension 16384) and FLUX (latent dimension about 64k), on a single NVIDIA A6000 GPU, at one bit per coefficient, sweeping the rate-distortion-perception curve.

The transmitted bitstream also stops depending on a precomputed combinatorial table. Selected indices form an unordered subset, and lexicographic ranking removes the permutation redundancy; H-DDCM instead computes binomial coefficients on the fly through an incremental recurrence or the hockey-stick identity, and groups candidate atoms so that group counts are sent first and local ranks follow, making combinatorial coding tractable at large dimensions. Turbo-DDCM's lexicographic rank and unrank relied on a dense precomputed table of binomial coefficients whose construction and storage scale poorly with dictionary size, becoming impractical at high dimensions. At FLUX scale the table costs about 1387 seconds to build and tens of GiB on disk in the larger configuration, while the recurrence pays no one-time setup and lowers total compress-plus-decompress time from 75.23 seconds to 68.50 seconds.

On video the framework attaches to a causal autoregressive flow model and adds a re-encoded-tail KV-cache refresh: at each continuation boundary, recently reconstructed pixel frames are re-encoded into a fresh KV-cache prefix, giving the next segment temporal context at no additional transmitted bits. This lets compression continue beyond the backbone's finite training context, enabling long-form, close to real-time streaming generative video compression on a single GPU. Extending the autoregressive cache beyond the training context degrades severely, while simply resetting the cache at each boundary discards temporal context and introduces discontinuities at segment boundaries. On UVG and MCL-JCV at 1280x720, PSNR, DOVER, FVMD, and encoding and decoding throughput are compared against HEVC, VVC, DCVC-UF, ZeroGVC, and Turbo-DDCM with both codebook sizes, with throughput measured on a single NVIDIA H200.

The report covers two experiment families: images on SD 2.1 (latent dimension 16384) and FLUX (latent dimension about 64k), and video on the Causal-Forcing backbone at 1280x720, with throughput measured on a single A6000 or H200. It suits readers following training-free generative compression, encoding into diffusion and flow sampling trajectories, and codebook scalability at large latent dimensions. On the video side, the re-encoded-tail KV-cache refresh and the first-step proxy residual initialization are ablated in the appendix, which is a starting point for reproduction.

On video, the consistency formulation uses no deterministic tail, so every step performs noise selection and carries bits; for the overcomplete dictionary, global top-k thresholding no longer exactly solves the sparse least-squares problem and follows Turbo-DDCM's practice, though direct synthesis and pseudo-inverse synthesis give nearly identical noise directions in practice. The first step builds a proxy residual from the source chunk's spatial mean, and the ablation shows that removing it can improve some aggregate metrics while struggling to stay temporally aligned with the input video. On images, steps crowd toward higher-noise timesteps at low bitrate and switch to even subsampling only once bitrate rises.