  Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion
model sampling at the cost of sample quality but lack a natural way to
trade-off quality for speed. To address this limitation, we propose Consistency
Trajectory Model (CTM), a generalization encompassing CM and score-based models
as special cases. CTM trains a single neural network that can -- in a single
forward pass -- output scores (i.e., gradients of log-density) and enables
unrestricted traversal between any initial and final time along the Probability
Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables
the efficient combination of adversarial training and denoising score matching
loss to enhance performance and achieves new state-of-the-art FIDs for
single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at
64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes,
both deterministic and stochastic, involving long jumps along the ODE solution
trajectories. It consistently improves sample quality as computational budgets
increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's
access to the score function can streamline the adoption of established
controllable/conditional generation methods from the diffusion community. This
access also enables the computation of likelihood. The code is available at
https://github.com/sony/ctm.
