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QCS-SGM+: Improved Quantized Compressed Sensing with Score-Based Generative Models
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Extends QCS-SGM to general (non-row-orthogonal) sensing matrices by approximating the pseudo-likelihood score for quantized compressed sensing with expectation propagation inside a score-based generative model posterior sampler.
Problem
Quantized compressed sensing with score-based generative priors breaks down for general sensing matrices because the likelihood score has no closed form unless the sensing matrix is (approximately) row-orthogonal.
Approach
Treat the pseudo-likelihood (partition function) as a Bayesian inference problem and approximate it with expectation propagation, decoupling the correlated Gaussian prior into factorized Gaussians via moment matching, yielding a closed-form likelihood score for general matrices; SVD makes the per-iteration matrix inversion cheap.
Key results
- QCS-SGM+ substantially outperforms QCS-SGM on 1-bit CS with ill-conditioned and correlated sensing matrices across MNIST, CIFAR-10 and CelebA in PSNR.
- QCS-SGM+ converges within 3-5 EP iterations; default IterEP=5 is used.
- Experiments run on one NVIDIA Tesla V100.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EP to approximate the likelihood score instead of QCS-SGM's diagonal approximation | QCS-SGM+ versus QCS-SGM · 1-bit CS on MNIST, CIFAR-10, and CelebA with ill-conditioned or correlated sensing matrices | PSNR | Helped |
| Use EP to approximate the likelihood score instead of QCS-SGM's diagonal approximation | QCS-SGM+ versus QCS-SGM · QCS on MNIST, CIFAR-10, and CelebA with general sensing matrices | SSIM | Helped |
| Add the scaling factor γ (ablation) | QCS-SGM+ · 1-bit CS on MNIST, CIFAR-10, and CelebA with ill-conditioned sensing matrices | PSNR | Helped |
| Use 3–5 EP iterations (ablation) | QCS-SGM+ · 1-bit CS on various datasets | PSNR | No clear effect |
| Add EP message passing | QCS-SGM+ versus QCS-SGM · Quantized compressed sensing | computational speed | Hurt |
Limitations
- QCS-SGM+ is computationally slower than QCS-SGM due to EP message passing.
- Still requires a large number of iterations to generate one posterior sample.
- Gains reported mainly for 1-bit and low-bit settings on image datasets.
Experimental setup
Datasets: MNIST CIFAR-10 CelebA
Benchmarks: MNIST CIFAR-10 CelebA
Metrics: PSNR SSIM
Baselines: QCS-SGM BIPG OneShot
Builds on: QCS-SGM NCSNv2 annealed Langevin dynamics expectation propagation CSGM
Closest papers by meaning
- GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling (NeurIPS 2026 · similarity 0.86)
- Sparse Bayesian Generative Modeling for Compressive Sensing (NeurIPS 2024 · similarity 0.85)
- SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression (ICLR 2024 · similarity 0.85)
- SqueezeLLM: Dense-and-Sparse Quantization (ICML 2024 · similarity 0.85)
- PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression (NeurIPS 2024 · similarity 0.84)
- QuIP$\#$: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks (ICML 2024 · similarity 0.84)
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