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Decoupling Training-Free Guided Diffusion by ADMM
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Proposes ADMMDiff, which decouples training-free guided diffusion into an unconditional diffusion subproblem and a guidance-loss subproblem linked by x = z and solved with ADMM, with a convergence analysis.
Problem
Conditional generation with off-the-shelf unconditional diffusion models guided by differentiable loss functions usually requires a hand-tuned weight to balance prior and guidance, which is task-dependent and hard to generalize.
Approach
Introduce an auxiliary variable z for guidance-refined samples, separate the diffusion prior (x) and guidance loss (z), and couple them via ADMM with a dual variable, so the balance is adaptive rather than set by a weight; the diffusion reverse step is shown to approximate the proximal operator of the prior term.
Key results
- On CelebA-HQ segmentation-map guidance, ADMMDiff reaches FID 30.18 versus 43.97 for the best baseline MPGD.
- On text-guided CelebA-HQ, ADMMDiff achieves CLIP score 26.85 versus 25.9 for FreeDoM.
- On linear inverse problems, ADMMDiff achieves best FID on 9 of 10 FFHQ/ImageNet tasks, e.g. FFHQ super-resolution FID 26.8 versus 39.35 for DPS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ADMMDiff instead of the strongest baseline | CelebA-HQ segmentation-map guidance · CelebA-HQ segmentation map | FID: 43.97 -> 30.18 | Helped |
| Use ADMMDiff instead of the strongest baseline | CelebA-HQ sketch guidance · CelebA-HQ sketch | FID: 60.56 -> 42.43 | Helped |
| Use ADMMDiff instead of the strongest baseline | CelebA-HQ text guidance · CelebA-HQ text | Distance: 10.46 -> 10.08 | Helped |
| Use ADMMDiff instead of the strongest baseline | CelebA-HQ text guidance · CelebA-HQ text | FID: 43.98 -> 43.84 | Helped |
| Use ADMMDiff instead of the strongest baseline | CelebA-HQ text guidance · CelebA-HQ text guidance | CLIP Score: 25.9 -> 26.85 | Helped |
| Use ADMMDiff instead of the strongest baseline | FFHQ diffusion restoration · FFHQ super-resolution (×4) | FID: 39.35 -> 26.8 | Helped |
| Use ADMMDiff instead of the strongest baseline | FFHQ diffusion restoration · FFHQ inpainting (box) | FID: 33.12 -> 24.97 | Helped |
| Use ADMMDiff instead of the strongest baseline | FFHQ diffusion restoration · FFHQ inpainting (random) | FID: 21.19 -> 22.04 | Hurt |
| Use ADMMDiff instead of the strongest baseline | FFHQ diffusion restoration · FFHQ Gaussian deblur | FID: 44.05 -> 27.98 | Helped |
| Use ADMMDiff instead of the strongest baseline | FFHQ diffusion restoration · FFHQ motion deblur | FID: 39.92 -> 25.11 | Helped |
| Use ADMMDiff instead of the strongest baseline | ImageNet diffusion restoration · ImageNet super-resolution (×4) | FID: 50.66 -> 49.97 | Helped |
| Use ADMMDiff instead of the strongest baseline | ImageNet diffusion restoration · ImageNet inpainting (box) | FID: 38.82 -> 37.47 | Helped |
Limitations
- Sampling cost is not reduced; the authors note acceleration as future work.
- Convergence proof relies on mild smoothness assumptions and small rho, and the inexact proximal approximations are only first-order.
- Not specially designed for linear inverse problems, where it wins most but not all metrics.
Experimental setup
Datasets: CelebA-HQ FFHQ ImageNet
Benchmarks: CelebA-HQ FFHQ 256 validation ImageNet 256 validation GMD trajectory motion prompts
Metrics: FID LPIPS CLIP score l2 distance to parsing/sketch outputs objective embedding distance PSNR SSIM
Baselines: DPS LGD-MC FreeDoM MPGD DDRM MCG PnP-ADMM Score-SDE ADMM-TV GMD
Builds on: ADMM PnP-ADMM Diffusion Posterior Sampling Tweedie's formula
Closest papers by meaning
- A Simple Approach to Unifying Diffusion-based Conditional Generation (ICLR 2025 · similarity 0.90)
- Understanding and Improving Training-free Loss-based Diffusion Guidance (NeurIPS 2024 · similarity 0.89)
- Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance (NeurIPS 2026 · similarity 0.89)
- Manifold Preserving Guided Diffusion (ICLR 2024 · similarity 0.89)
- REG: Rectified Gradient Guidance for Conditional Diffusion Models (ICML 2025 · similarity 0.89)
- DEFT: Efficient Fine-tuning of Diffusion Models by Learning the Generalised $h$-transform (NeurIPS 2024 · similarity 0.88)
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