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Characteristic Guidance: Non-linear Correction for Diffusion Model at Large Guidance Scale
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Proposes characteristic guidance, a training-free non-linear correction to classifier-free guidance derived from the method of characteristics on the score Fokker-Planck equation, improving sample quality at large guidance scales.
Problem
Classifier-free guidance linearly combines conditional and unconditional DDPM outputs, which deviates from the score Fokker-Planck equation at large guidance scales, causing saturation, color/exposure irregularities, and loss of diversity.
Approach
Adds a non-linear correction term Δx, solved by fixed-point iteration under a harmonic ansatz (Laplacian of the score is negligible), so the guided denoiser approximately satisfies the FP equation with no mixing error; the method is training-free and compatible with existing samplers.
Key results
- On CIFAR-10 with DDIM (50 steps), characteristic guidance lowers FID vs classifier-free guidance at every scale (e.g., 27.04 vs 24.77 at omega=6 is CH better; CH FID 24.77 vs CF 27.04 at omega=6), with comparable IS.
- On Gaussian toy experiments, characteristic guidance gives better KL divergence than classifier-free guidance for all four samplers, especially for ODE-based samplers where CF suffers severe bias and diversity loss.
- On ImageNet 256 latent diffusion, CH shows a rightward IS-FID shift, meaning it reaches a given IS at lower guidance scale, but FID is worse than CF.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use characteristic guidance instead of classifier-free guidance | CIFAR-10 DDPM · CIFAR-10, DDIM 50 steps, ω=6.0 | FID: 27.04 -> 24.77 | Helped |
| Use characteristic guidance instead of classifier-free guidance | CIFAR-10 DDPM · CIFAR-10, DPM++2M 50 steps, ω=6.0 | FID: 23.47 -> 21.46 | Helped |
| Use characteristic guidance instead of classifier-free guidance | CIFAR-10 DDPM · CIFAR-10, DDIM 50 steps, ω=6.0 | IS: 8.85 -> 8.86 | No clear effect |
| Use characteristic guidance instead of classifier-free guidance | CIFAR-10 DDPM · CIFAR-10, DPM++2M 50 steps, ω=6.0 | IS: 9.33 -> 9.38 | No clear effect |
Surprising findings
- On ImageNet 256 latent diffusion, CH achieves higher IS but worse FID than CF, so the usual FID-based evaluation gives a mixed picture.
- Classifier-free guidance with ODE-based samplers shows severe bias and catastrophic loss of diversity on Gaussian toy models.
Limitations
- Iterative fixed-point solving requires multiple extra denoiser evaluations, making it slow without better regularization.
- The harmonic ansatz is only approximate for real image distributions and fails in overlap regions of mixtures and near phase transitions.
- FID is a questionable metric for guided sampling since the target is p(x|c,omega) rather than marginal p(x).
Experimental setup
Datasets: CIFAR-10 ImageNet 256 Gaussian toy distributions Landau-Ginzburg magnet simulation
Benchmarks: CIFAR-10 ImageNet 256
Metrics: FID IS KL divergence NLL
Baselines: classifier-free guidance DDIM DPM++2M dynamic thresholding
Builds on: classifier-free guidance classifier guidance DDPM DDIM dynamic thresholding
Closest papers by meaning
- Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance (NeurIPS 2026 · similarity 0.90)
- Theoretical insights for diffusion guidance: A case study for Gaussian mixture models (ICML 2024 · similarity 0.90)
- Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models (ICLR 2025 · similarity 0.90)
- Feedback Guidance of Diffusion Models (NeurIPS 2025 · similarity 0.90)
- Adaptive Guidance: Training-free Acceleration of Conditional Diffusion Models (AAAI 2025 · similarity 0.90)
- Tortoise and Hare Guidance: Accelerating Diffusion Model Inference with Multirate Integration (NeurIPS 2025 · similarity 0.90)
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