Turbo-DDCM: Efficient Diffusion Image Compression

• Turbo-DDCM is an efficient zero-shot diffusion-based image compression method that employs closed‐form multi-atom codebook selection to reduce computational overhead.
• It substantially cuts reverse diffusion steps by up to 95%, while offering priority-aware and distortion-controlled variants for enhanced region-of-interest fidelity and targeted PSNR control.
• Experimental results show Turbo-DDCM achieves competitive PSNR, LPIPS, and FID metrics at dramatically lower runtimes compared to traditional diffusion codecs.

Turbo-DDCM is an efficient and flexible zero-shot diffusion-based image compression methodology that advances prior Denoising Diffusion Codebook Models (DDCMs) by introducing a closed-form, multi-atom codebook selection and improved bitstream protocols. Turbo-DDCM substantially reduces the number of reverse diffusion steps required for image reconstruction, thereby enabling orders-of-magnitude speedup over existing zero-shot diffusion codecs, while retaining competitive perceptual and distortion metrics against state-of-the-art methods. The design offers two notable variants—priority-aware and distortion-controlled compression—that allow explicit user control over region-of-interest and distortion targets within the zero-shot paradigm (Vaisman et al., 9 Nov 2025).

1. Theoretical Foundations and Connection to DDCMs

Turbo-DDCM builds upon the paradigm of denoising diffusion probabilistic models (DDPMs), leveraging their iterative noising and denoising stochastic processes. The forward process applies a sequence of Gaussian noise injections: $$x_t = \sqrt{\bar\alpha_t}\,x_0 + \sqrt{1 - \bar\alpha_t}\,\epsilon, \quad \epsilon \sim \mathcal{N}(0, I)$$ with $\bar\alpha_t = \prod_{s=1}^t \alpha_s$ encoding the cumulative product of noise variance schedules.

The DDCM framework replaces the random Gaussian noise in the reverse generative step,

$$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$

with disambiguating noise vectors $z_t^{(k)}$ from a reproducible codebook of $K$ atoms, enabling discrete bit-indexed control over the latent diffusion trajectory. Standard DDCM with $M=1$ selects at each step the codebook atom maximizing alignment with the stepwise residual $r_t = x_0 - \hat x_{0|t}$, storing $\lceil \log_2 K \rceil$ bits per denoising step. Multi-atom DDCM generalizes this via matching pursuit (MP), selecting $M>1$ atoms per step in a sequential manner, but at significant computational cost.

Turbo-DDCM advances this by performing simultaneous closed-form selection of $M$ atoms, optimizing

$\bar\alpha_t = \prod_{s=1}^t \alpha_s$0

where $\bar\alpha_t = \prod_{s=1}^t \alpha_s$1 collects the $\bar\alpha_t = \prod_{s=1}^t \alpha_s$2 codebook atoms and $\bar\alpha_t = \prod_{s=1}^t \alpha_s$3 is a quantized coefficient set. Under near-orthogonality (typical of i.i.d. Gaussian codebooks), this reduces to top-$\bar\alpha_t = \prod_{s=1}^t \alpha_s$4 selection by the absolute inner product with the residual, assigning $\bar\alpha_t = \prod_{s=1}^t \alpha_s$5 as the coefficient for the selected atoms ($\bar\alpha_t = \prod_{s=1}^t \alpha_s$6), followed by normalization. This eliminates the need for iterative search and drastically reduces the required number of denoiser calls.

2. Algorithmic Workflow and Bitstream Protocol

Turbo-DDCM’s encoding and decoding process consists of:

• Encoding steps ($\bar\alpha_t = \prod_{s=1}^t \alpha_s$7):

1. Compute the residual $\bar\alpha_t = \prod_{s=1}^t \alpha_s$8.
2. Calculate inner products $\bar\alpha_t = \prod_{s=1}^t \alpha_s$9 for all codebook atoms.
3. Select the top-$$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$0 indices in $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$1.
4. Set coefficients $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$2 for selected $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$3, else 0.
5. Serialize the subset index as its lexicographic rank ($$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$4 bits) and the $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$5 coefficient values ($$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$6 bits).
6. Update $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$7 by injecting the normalized linear combination of atoms: $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$8.

• Bit Protocol:
  • Transmit lexicographic rank of subset $$x_{t-1} = \mu_\theta(x_t, t) + \sigma_t\,z, \quad z \sim \mathcal{N}(0, I),$$9 (size $z_t^{(k)}$0 from $z_t^{(k)}$1), not ordered indices, eliminating permutation redundancy.
  • For $z_t^{(k)}$2 steps, total bits per pixel:

  $z_t^{(k)}$3 - No bits are transmitted for the $z_t^{(k)}$4 final deterministic DDIM steps, which conclude image restoration.

• Computational Complexity:

  • Each encoding/decoding step costs $z_t^{(k)}$5, enabling feasible settings ($z_t^{(k)}$6, $z_t^{(k)}$7) with total $z_t^{(k)}$8–30, i.e., a 95% denoiser call reduction from DDCM ($z_t^{(k)}$9–1000).
• Decoding: Follows the identical reverse process, reconstructing $K$0 with codebook indices and coefficients provided by the bitstream.

3. Flexible Compression Variants

Turbo-DDCM supports two algorithmic extensions:

Priority-Aware Turbo-DDCM:

Allows explicit focus on user-specified image regions of interest (ROI), by replacing the residuals in step (5) with a masked version $K$1, $K$2. This increases atom allocation where fidelity is prioritized, without altering bitrate or runtime. Empirical results indicate substantial ROI fidelity gains at fixed BPP.

Distortion-Controlled Turbo-DDCM:

Addresses inherent PSNR variability at fixed bitrates in zero-shot compression by exploiting a strong empirical linear correlation between Turbo-DDCM’s PSNR and the lossless JPEG compressed file size: $K$3 Linear predictors trained across BPPs guide per-image selection of minimal $K$4 achieving a target PSNR. On test images, this reduces PSNR root-mean-square error by over 40% compared to naïve BPP selection.

4. Experimental Results and Benchmarks

Turbo-DDCM was evaluated on the Kodak24 ($K$5) and DIV2K ($K$6) datasets, in comparison with other zero-shot and trained methods. Table 1 at BPP $K$7 reports:

Method	PSNR (dB)	LPIPS	FID	Time (s/img)
BPG	24.1	0.25	120	0.1
PerCo (SD)	25.6	0.15	22	1.0
DiffC	25.2	0.18	30	10
DDCM	24.8	0.20	45	65
Turbo-DDCM	25.3	0.17	20	1.5

Turbo-DDCM matches or surpasses all zero-shot methods in PSNR, LPIPS, and FID, while running 3×–40× faster. Compared to trained models, only PerCo (SD) slightly outperforms in PSNR, but with lower perceptual quality (higher FID).

Ablation studies demonstrate:

• Turbo-DDCM’s top-$K$8 thresholded atom combinations result in equal or better angular alignment to the residual than DDCM MP, with performance continuing to improve as $K$9 increases (unlike MP, which plateaus).
• Empirical runtime scaling is $M=1$0–$M=1$1× faster than DDCM + MP across practical $M=1$2.

5. Limitations and Prospects

Turbo-DDCM introduces significant practical benefits, but several limitations remain:

• At high bitrates, the codec’s underlying latent-diffusion backbone yields diminishing returns in PSNR, suggesting encoder/decoder distortion floors. End-to-end image-space training could potentially ameliorate this ceiling.
• Current reverse processes require $M=1$320–30 diffusion steps; further efficiency gains may be possible by learning direct mappings from noisy latents to $M=1$4 ("one-step zero-shot solvers").
• A formal information-theoretic analysis of the limits and optimality of codebook-based zero-shot encoding remains open.

This suggests future research direction toward tighter latent/image coupling, adaptive codebook designs, and theoretical characterizations of zero-shot diffusion compression.

6. Context and Significance

Turbo-DDCM enables zero-shot diffusion-based compression to become a practical tool for both research and applied imaging, offering sub-2s per-image decode times and fine-grained control of bitrate, ROI, and distortion without dataset-specific training. The method’s closed-form multi-atom codebook selection and bit-efficient indexing protocol lead to an approximately 95% reduction in denoiser calls and a $M=1$540% BPP reduction over naïve bit-packing approaches, shifting the zero-shot diffusion codec paradigm from an academic concept toward routine deployment in bandwidth-sensitive imaging scenarios.