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Cross-fluctuation phase transitions reveal sampling dynamics in diffusion models
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Uses centered-moment cross-fluctuations (CKA-style normalized cross-fluctuation) to detect discrete merger transitions in diffusion trajectories, and applies the detected times to accelerate sampling, class-conditional and rare-class generation, zero-shot classification and style transfer.
Problem
Sampling dynamics of diffusion models are a black box; it is unclear when class or event distributions become distinguishable or merge during forward/reverse diffusion, and how to use this to guide sampling.
Approach
Defines normalized cross-fluctuations (centered moments, with n=2 reducing to CKA between conditional covariances) over user-defined events and treats the first near-1 value as a discrete merger/phase transition, which sets guidance windows, start times, and weighting intervals for diffusion models.
Key results
- Starting reverse sampling at detected convergence index reduces DiT-XL/2 ImageNet steps from 250 to 175 with FID 3.37 vs 3.42.
- Merger-aware interval guidance improves DiT-XL/2 ImageNet FID from 3.22 to 2.86 and DDPM CIFAR10 FID from 3.32 to 3.01.
- Truncated inverse-SNR weighting raises SD zero-shot ImageNet accuracy from 54.96 to 65.28 percent.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Start reverse sampling at the detected convergence time instead of the full horizon | DDPM on MNIST · MNIST | FID: 2.27\pm0.19 -> 2.29\pm0.17 | No clear effect |
| Start reverse sampling at the detected convergence time instead of the full horizon | DDPM on MNIST · MNIST | steps: 1000 -> 600 | Helped |
| Start reverse sampling at the detected convergence time instead of the full horizon | DiT-XL/2 · ImageNet | FID: 3.42\pm0.21 -> 3.37\pm0.31 | Helped |
| Start reverse sampling at the detected convergence time instead of the full horizon | DDPM · CIFAR-10 | FID: 3.62\pm0.35 -> 3.47\pm0.34 | Helped |
| Use merger-detected class-specific guidance windows instead of the baseline IG schedule | Interval Guidance · ImageNet | FID: 3.22 \pm 0.16 -> 2.86 \pm 0.15 | Helped |
| Use merger-detected class-specific guidance windows instead of the baseline IG schedule | Interval Guidance · MNIST | FID: 2.15 \pm 0.06 -> 1.99 \pm 0.11 | Helped |
| Use merger-detected class-specific guidance windows instead of the baseline IG schedule | Interval Guidance · CIFAR-10 | FID: 3.32 \pm 0.25 -> 3.01 \pm 0.14 | Helped |
| Use merger-aware timestep bounds with uniform weighting | Stable Diffusion zero-shot classification · ImageNet | accuracy: 54.96\!\pm\!0.67 -> 57.91\!\pm\!0.53 | Helped |
| Use merger-aware timestep bounds with truncated inverse-SNR weighting rather than uniform weighting | Stable Diffusion zero-shot classification · CIFAR-10 | accuracy: 84.67\!\pm\!1.23 -> 88.38\!\pm\!0.43 | Helped |
| Use merger-aware timestep bounds with truncated inverse-SNR weighting rather than uniform weighting | Stable Diffusion zero-shot classification · Oxford-IIIT Pets | accuracy: 82.87\!\pm\!0.39 -> 89.15\!\pm\!0.26 | Helped |
| Use the source-distribution merger time to choose reverse denoising start time | Zero-shot style transfer · OxfordIIITPets, Ghibli | PSNR: 25.67 \pm 1.14 -> 28.71 \pm 0.86 | Helped |
| Use merger-aware interval guidance with corrupted exemplars instead of merger-aware interval guidance alone (ablation) | Rare-class generation with Stable Diffusion · iNaturalist | CLIP Similarity: 0.24 ± 0.02 -> 0.27 ± 0.01 | Helped |
Surprising findings
- Merger time predicts convergence of the data distribution surprisingly well compared with an unrelated Brownian equilibrium-time theorem.
- Truncated inverse-SNR weighting outperforms uniform weighting for zero-shot classification, suggesting corrupted marginals are most discriminative shortly before class merger.
Limitations
- Analysis assumes a variance-preserving noise schedule; non-VP schedules such as EDM are not covered.
- Uses isotropic-noise assumptions and n=2 (covariance) statistics; higher-order fluctuations only partially explored.
- Style transfer relies on a Fourier regularity assumption and bijectivity of the style map.
Experimental setup
Datasets: MNIST CIFAR-10 ImageNet CUB-200 iNaturalist 2019 Oxford-IIIT Pets AFHQv2
Benchmarks: MNIST CIFAR-10 ImageNet CUB-200 iNaturalist 2019 Oxford-IIIT Pets AFHQv2
Metrics: FID Precision Recall Density Coverage CLIP similarity accuracy PSNR MSE
Baselines: Interval guidance DiT-XL/2 full sampling SD uniform zero-shot weighting CLIP RN-50 OpenCLIP ViT-H/14 SD Edit
Builds on: Interval guidance ILVR DDPM Score-based SDE Centered Kernel Alignment
Closest papers by meaning
- On the Error Correcting Effects of Stochasticity in Discrete Diffusion (NeurIPS 2026 · similarity 0.89)
- Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling (NeurIPS 2026 · similarity 0.88)
- Tracing the Roots: Leveraging Temporal Dynamics in Diffusion Trajectories for Origin Attribution (NeurIPS 2025 · similarity 0.88)
- Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics (ICLR 2025 · similarity 0.88)
- Diffusion Path Samplers via Sequential Monte Carlo (NeurIPS 2026 · similarity 0.88)
- Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference (NeurIPS 2024 · similarity 0.87)
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