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Simplifying, Stabilizing and Scaling Continuous-time Consistency Models
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Simplifies (TrigFlow unifies EDM and flow matching) and stabilizes continuous-time consistency models (sCM) with architecture, parameterization, and objective fixes, scaling them to 1.5B parameters on ImageNet 512x512 with two-step FIDs near teacher diffusion models.
Problem
Continuous-time consistency models have been hard to train due to instability, and prior CMs rely on discrete timesteps with discretization errors and hand-tuned schedules and weights; scaling them to large models has not been demonstrated.
Approach
TrigFlow reparameterizes diffusion with trigonometric noise schedule (x_t = cos t x0 + sin t z) unifying EDM and flow matching; stabilizing changes include identity time transformation, positional time embeddings, adaptive double normalization, JVP rearrangement, tangent normalization, and adaptive weighting for the continuous-time CM objective.
Key results
- Two-step sCT achieves FID 2.06 on unconditional CIFAR-10 and 1.48 on ImageNet 64x64 (teacher FIDs 2.01 and 1.33).
- Two-step sCD on ImageNet 512x512 reaches FID 1.88 with 1.5B params (teacher EDM2-XXL FID 1.73 as reimplemented), within 10% of the teacher.
- Continuous-time CMs outperform discrete-time CMs across all discretization step counts N in the ablation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use continuous-time CMs rather than discrete-time CMs (ablation) | sCM · CIFAR-10 and ImageNet 64×64 | FID | Helped |
| Increase the number of discretization steps N (ablation) | discrete-time CMs · CIFAR-10 | FID | Mixed |
| Normalize the tangent (ablation) | continuous-time CMs · CIFAR-10 | training stability | Helped |
| Clip the tangent to [-1, 1] (ablation) | continuous-time CMs · CIFAR-10 | training stability | Helped |
| Use TrigFlow formulation (ablation) | sCM · CIFAR-10 | FID | Helped |
| Use adaptive weighting instead of manually designed weighting (ablation) | continuous-time CMs · CM training | empirical performance | Helped |
| Use identity time transformation c_noise(t)=t (ablation) | continuous-time CMs · CM training | training stability | Helped |
| Use positional time embeddings instead of larger-scale Fourier embeddings (ablation) | continuous-time CMs · CM training | training stability | Helped |
| Use adaptive double normalization instead of AdaGN (ablation) | continuous-time CMs · CM training | training stability | Helped |
| Apply tangent warmup (ablation) | sCD · sample quality | FID | No clear effect |
| Scale sCT from smaller to larger models on ImageNet 512×512 | sCT · ImageNet 512×512 | FID | Hurt |
Surprising findings
- sCT is less effective than sCD in latent space at ImageNet 512x512, which the authors attribute to higher CT variance.
- VSD produces mode collapse at high guidance, with precision rising and recall falling, yielding worse FID than two-step sCD.
Limitations
- Samples still show artifacts on class-conditional ImageNet; FID does not capture all semantic detail.
- sCD depends heavily on a pretrained diffusion teacher, restricting architectures; sCM requires architecture modifications that may not suit diffusion architectures.
- sCT is less effective than sCD in latent space at 512x512 due to higher training variance.
Experimental setup
Datasets: CIFAR-10 ImageNet 64x64 ImageNet 512x512
Benchmarks: CIFAR-10 ImageNet 64x64 ImageNet 512x512
Metrics: FID precision recall NFE
Baselines: iCT iCT-deep ECT CD (LPIPS) TRACT PD StyleGAN-XL VAR EDM2 VSD
Builds on: consistency models EDM flow matching EDM2 variational score distillation
Closest papers by meaning
- Consistency Models Made Easy (ICLR 2025 · similarity 0.91)
- Truncated Consistency Models (ICLR 2025 · similarity 0.91)
- Sampling is as easy as keeping the consistency: convergence guarantee for Consistency Models (ICML 2024 · similarity 0.91)
- Phased Consistency Models (NeurIPS 2024 · similarity 0.90)
- Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme (ICML 2025 · similarity 0.90)
- Theory of Consistency Diffusion Models: Distribution Estimation Meets Fast Sampling (ICML 2024 · similarity 0.90)
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