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Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion
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Proposes Consistency Trajectory Model (CTM), which learns anytime-to-anytime jumps along the PF ODE with a single network, combining soft consistency distillation with DSM and adversarial losses, and enables gamma-sampling that trades quality for speed.
Problem
Consistency models accelerate diffusion sampling but lose sample quality as the number of steps increases and lack a speed-quality trade-off; score-based solvers are limited by discretization error at few steps.
Approach
A single network G(x_t,t,s) predicts the PF ODE solution from any time t to any s<=t, parameterized via g so that G(x,t,t) is identity and g(x,t,t) equals the denoiser; trained with soft consistency matching (random intermediate u), plus DSM and GAN losses, and sampled with gamma-sampling that alternates forward and backward jumps.
Key results
- CTM achieves FID 1.98 unconditional and 1.73 conditional on CIFAR-10 with 1 NFE, and FID 1.63 with 2 NFE.
- On ImageNet 64x64, CTM reaches FID 1.92 with 1 NFE and 1.73 with 2 NFE, improving on CM's 6.20 and 4.70.
- Training without a pre-trained diffusion model reaches FID 2.39 at 1 NFE on unconditional CIFAR-10.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace CD with CTM at 1 NFE | CIFAR-10 unconditional generation · CIFAR-10 unconditional | FID: 3.55 -> 1.98 | Helped |
| use CTM instead of EDM | CIFAR-10 conditional generation at 1 NFE · CIFAR-10 conditional | FID: 1.82 -> 1.73 | Helped |
| increase CTM sampling from 1 to 2 NFE | CIFAR-10 conditional generation · CIFAR-10 conditional | FID: 1.73 -> 1.63 | Helped |
| replace EDM with CTM at 1 NFE | ImageNet 64x64 generation · ImageNet 64x64 | FID: 2.44 -> 1.92 | Helped |
| add adversarial GAN loss (ablation) | CTM · CIFAR-10 image generation | sample quality | Helped |
| add DSM loss (ablation) | CTM · CIFAR-10 image generation at large NFE | sample quality | Helped |
| add DSM loss (ablation) | CTM · CIFAR-10 image generation at small NFE | sample quality | No clear effect |
| replace local consistency matching with soft consistency matching (ablation) | CTM · image generation | sample quality | Helped |
| use gamma=1 multistep sampling instead of gamma approximately 0 sampling (ablation) | CTM · image generation as NFE increases | FID | Hurt |
| train without GAN loss (ablation) | CTM · CIFAR-10 image generation | FID | Hurt |
| replace the ODE solver-oriented parameterization with EDM-type parameterization (ablation) | CTM · training stability | training stability | Hurt |
Surprising findings
- Retraining CM with its official code gives FID 10.53 unconditional on CIFAR-10, far worse than the reported 3.55.
Limitations
- Results depend on a pre-trained teacher diffusion model for the distillation target (except the no-pretrained variant).
- The optimal gamma depends on the practical use case and requires empirical tuning.
Experimental setup
Datasets: CIFAR-10 ImageNet 64x64
Benchmarks: CIFAR-10 ImageNet 64x64
Metrics: FID IS NLL recall
Baselines: EDM Consistency Models (CM) Progressive Distillation BOOT StyleGAN-XL DDIM Score SDE
Builds on: consistency models EDM VQGAN StyleGAN-XL
Closest papers by meaning
- Truncated Consistency Models (ICLR 2025 · similarity 0.90)
- Generalized Consistency Trajectory Models for Image Manipulation (ICLR 2025 · similarity 0.90)
- SCott: Accelerating Diffusion Models with Stochastic Consistency Distillation (AAAI 2025 · similarity 0.90)
- Improving Consistency Models with Generator-Augmented Flows (ICML 2025 · similarity 0.89)
- Consistency Diffusion Bridge Models (NeurIPS 2024 · similarity 0.89)
- Simplifying, Stabilizing and Scaling Continuous-time Consistency Models (ICLR 2025 · similarity 0.89)
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