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Progressive Compression with Universally Quantized Diffusion Models
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Proposes Universally Quantized Diffusion Models (UQDM), a diffusion model with uniform forward noise whose negative ELBO equals the end-to-end progressive compression cost via universal quantization, enabling tractable progressive image coding.
Problem
Gaussian diffusion-based progressive compression requires channel simulation of Gaussian samples whose runtime is exponential in the information communicated, making it intractable in practice.
Approach
Replace Gaussian forward posterior with a uniform distribution matched in mean and variance, and model the reverse process as a learned logistic/Gaussian density convolved with uniform noise, so each step can be coded efficiently with universal quantization; learn per-coordinate reverse variance.
Key results
- On CIFAR10, UQDM outperforms JPEG and JPEG2000 across all bit-rates in PSNR and FID, and beats BPG in PSNR at higher bit-rates while closely matching BPG in FID.
- On ImageNet 64x64, UQDM with denoised predictions outperforms JPEG and JPEG2000 and is comparable to or slightly better than CTC, with gains continuing at higher bit-rates where other codecs plateau.
- Learning per-coordinate reverse-process variance significantly improves the lossless NELBO on swirl data across all T, with an optimal T around 5.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| learn the reverse-process variance (ablation) | UQDM · Swirl toy data | NELBO | Helped |
| increase T beyond 5 (ablation) | UQDM · Swirl toy data | NELBO | Hurt |
| increase T (ablation) | UQDM · Swirl toy data | sample quality | Helped |
| initialize fixed-variance UQDM with pretrained VDM weights (ablation) | UQDM · Swirl toy data | NELBO | No clear effect |
| finetune UQDM initialized with pretrained VDM weights (ablation) | UQDM · Swirl toy data | NELBO | No clear effect |
| use denoised prediction instead of ancestral sampling (ablation) | UQDM · ImageNet 64 × 64 | FID | Hurt |
| use flow-based reconstruction instead of denoised prediction (ablation) | UQDM · ImageNet 64 × 64 | FID | Helped |
| increase denoising network size (ablation) | UQDM · ImageNet 64 × 64 | bit-rate | Helped |
| use a learned noise schedule instead of a linear noise schedule (ablation) | UQDM · Image compression | compression performance | No clear effect |
| use logistic reverse density instead of Gaussian reverse density (ablation) | UQDM · Image compression | compression performance | No clear effect |
| use UQDM instead of JPEG or JPEG2000 | image compression · CIFAR10 | PSNR | Helped |
| use UQDM instead of JPEG, JPEG2000, or CTC | image compression · ImageNet 64 × 64 | compression performance | Helped |
Surprising findings
- Learning the reverse-process variance is essential; a theoretical lower bound of about (1/3)log2 per step arises with fixed variance, causing overhead per diffusion step.
- Sample quality improves monotonically with T on swirl data even though compression performance worsens for T > 5.
Limitations
- Learned reverse-process variance makes entropy coding very slow (about 5 minutes per CIFAR image) in the current implementation.
- Performance gap remains to the hypothetical Gaussian diffusion (VDM) with REC; compression degrades for larger T.
- Only a small number of diffusion steps (T about 4) works best for compression, and end-to-end training with large T is not explored.
Experimental setup
Datasets: CIFAR10 ImageNet 64x64 swirl toy data
Benchmarks: CIFAR10 ImageNet 64x64 swirl toy data
Metrics: PSNR FID bits per dimension bits per pixel sliced Wasserstein distance
Baselines: JPEG JPEG2000 BPG CTC CDC VDM (hypothetical REC) DiffC-A DiffC-F
Builds on: VDM DDIM DiffC (Gaussian diffusion progressive compression) universal quantization minimal random coding
Closest papers by meaning
- Bridging the Gap between Gaussian Diffusion Models and Universal Quantization for Image Compression (CVPR 2025 · similarity 0.94)
- OSCAR: One-Step Diffusion Codec Across Multiple Bit-rates (NeurIPS 2025 · similarity 0.91)
- Compressed Image Generation with Denoising Diffusion Codebook Models (ICML 2025 · similarity 0.90)
- Lossy Compression with Pretrained Diffusion Models (ICLR 2025 · similarity 0.89)
- Ultra Lowrate Image Compression with Semantic Residual Coding and Compression-aware Diffusion (ICML 2025 · similarity 0.89)
- BitsFusion: 1.99 bits Weight Quantization of Diffusion Model (NeurIPS 2024 · similarity 0.88)
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