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Warm Diffusion: Recipe for Blur-Noise Mixture Diffusion Models
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Proposes Warm Diffusion, a blur-noise mixture diffusion model (BNMD) that jointly applies Gaussian blur and noise with a divide-and-conquer denoiser/deblurrer parameterization and a BNR of 0.5, improving FID over EDM on CIFAR-10 and FFHQ.
Problem
Hot diffusion (noise-only) underexploits spectral dependency between low- and high-frequency image content, while cold diffusion (blur-only) causes out-of-manifold reverse trajectories and poor sample quality; the trade-off between the two is unclear.
Approach
Jointly corrupt images with blur and noise in the forward process, controlled by a Blur-to-Noise Ratio (BNR), and split the score/mean prediction into a denoiser (predicts blurry image) and a deblurrer (predicts high-frequency residual); BNR is chosen via power spectral density analysis (BNR=0.5).
Key results
- Unconditional CIFAR-10 FID 1.85 and IS 10.02 at 35 NFE, versus EDM's 1.97 FID and 9.78 IS.
- Class-conditional CIFAR-10 FID 1.68 (vs. EDM 1.79) and FFHQ 64x64 FID 2.29 at 79 NFE (vs. EDM 2.53).
- Ablation shows BNR=0.5 gives the best FID (1.85); BNR=10 degrades FID to 11.97, supporting the manifold-shift trade-off.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BNR=0.5 instead of BNR=0 (ablation) | Warm Diffusion on CIFAR-10 · CIFAR-10 (NFE=35) | FID: 1.97 -> 1.85 | Helped |
| Use BNR=0.1 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 1.97 | Hurt |
| Use BNR=0.3 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 1.90 | Hurt |
| Use BNR=0.65 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 1.91 | Hurt |
| Use BNR=1 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 2.01 | Hurt |
| Use BNR=2 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 2.57 | Hurt |
| Use BNR=10 instead of BNR=0.5 (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 11.97 | Hurt |
| Replace the two-branch method with one branch predicting x₀ directly (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 13.19 | Hurt |
| Replace divide-and-conquer residual parameterization with two branches predicting clean and blurry signals (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 1.85 -> 1.98 | Hurt |
| Use the proposed divide-and-conquer parameterization instead of a single blurry-signal branch (ablation) | Warm Diffusion · CIFAR-10 (NFE=35) | FID: 9.09 -> 1.85 | Helped |
| Use Warm Diffusion instead of PFGM++ | Unconditional CIFAR-10 generation · Unconditional CIFAR-10 | FID: 1.91 -> 1.85 | Helped |
| Use Warm Diffusion instead of PFGM++ | Class-conditional CIFAR-10 generation · Class-conditional CIFAR-10 | FID: 1.74 -> 1.68 | Helped |
Surprising findings
- Higher BNR (approaching cold diffusion) degrades sample quality sharply, with BNR=10 giving FID 11.97 on CIFAR-10 at 35 NFE.
- Re-implementing Blurring Diffusion's BNR schedule under the same setup gives FID 12.97 at 35 NFE, improving only with many more steps.
Limitations
- Relies on BNR selected heuristically from spectral analysis of images and Gaussian noise; the 0.5 value is empirical.
- Higher BNR requires more sampling steps to stay on the data manifold, limiting efficiency under small step budgets.
- Evaluation limited to image generation on CIFAR-10, FFHQ, and LSUN-church.
Experimental setup
Datasets: CIFAR-10 FFHQ LSUN-church
Benchmarks: CIFAR-10 FFHQ LSUN-church
Metrics: FID IS NFE
Baselines: EDM EDM-ES STF PFGM++ Cold Diffusion IHDM Blurring Diffusion Denoising Diffusion
Builds on: EDM DDIM Cold Diffusion Blurring Diffusion Inverse Heat Dissipation (IHDM)
Closest papers by meaning
- BlurDM: A Blur Diffusion Model for Image Deblurring (NeurIPS 2025 · similarity 0.90)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.90)
- Ambient Diffusion Omni: Training Good Models with Bad Data (NeurIPS 2025 · similarity 0.90)
- Faster Diffusion: Rethinking the Role of the Encoder for Diffusion Model Inference (NeurIPS 2024 · similarity 0.89)
- Diffusion Models With Learned Adaptive Noise (NeurIPS 2024 · similarity 0.89)
- Diffusion Models Without Attention (CVPR 2024 · similarity 0.89)
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