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Guidance with Spherical Gaussian Constraint for Conditional Diffusion

ICML 2024 · Image generation › Fast diffusion sampling · approach: Guidance for conditional diffusion · 4 citations (OpenAlex)

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Proposes DSG, a training-free plug-in that constrains loss-guided diffusion updates to a spherical Gaussian shell (closed-form solution), reducing manifold deviation and allowing larger guidance steps for DPS, Freedom, and UGD.

Problem

Training-free loss-guided conditional diffusion degrades sample quality and requires small guidance step sizes (slow sampling), attributed to manifold deviation of intermediate samples caused by the Jensen gap and linear manifold assumptions.

Approach

Derive a lower bound on the Jensen gap of loss guidance, then restrict the guidance update to a hypersphere determined by the unconditional DDIM mean and noise scale (high-dimensional Gaussian concentration), giving a closed-form normalized-gradient update that can be added to existing training-free methods with a few lines of code.

Key results

• On FFHQ inpainting, DPS+DSG reaches LPIPS 0.115 and FID 15.77 versus DPS 0.212 and 21.19.
• With only 20 DDIM steps on FFHQ inpainting, DPS+DSG achieves PSNR 27.53 versus 12.08 for DPS.
• In FaceID guidance on CelebA-HQ, Freedom+DSG improves FaceID score from 0.545 to 0.371 (lower is better as reported) and FID from 39.61 to 34.29.

Measured effects reported in the paper

Surprising findings

• The paper states the method can use step sizes exceeding 400x compared with prior training-free methods at t=T with eta=1.
• DPS degrades sharply with fewer denoising steps (e.g., 20 steps), while DPS+DSG remains robust.

Limitations

• Reduces sample diversity because the random noise direction is replaced by a deterministic guidance direction, mitigated only by a guidance rate.
• Approximating the high-dimensional Gaussian by a hypersphere may reduce diversity.
• The Jensen-gap lower bound relies on strong convexity assumptions that are only argued heuristically for general losses.

Experimental setup

Datasets: FFHQ 256x256 ImageNet 256x256 WikiArt CelebA-HQ

Benchmarks: FFHQ 256x256 linear inverse problems ImageNet 256x256 linear inverse problems WikiArt style guidance CelebA-HQ FaceID guidance

Metrics: LPIPS FID SSIM PSNR KID FaceID score

Baselines: DPS MCG PnP-ADMM Score-SDE DDRM LGD Freedom UGD DDNM MPGD

Builds on: DPS Freedom UGD MCG LGD

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