  Diffusion-based generative models excel in unconditional generation, as well
as on applied tasks such as image editing and restoration. The success of
diffusion models lies in the iterative nature of diffusion: diffusion breaks
down the complex process of mapping noise to data into a sequence of simple
denoising tasks. Moreover, we are able to exert fine-grained control over the
generation process by injecting guidance terms into each denoising step.
However, the iterative process is also computationally intensive, often taking
from tens up to thousands of function evaluations. Although consistency
trajectory models (CTMs) enable traversal between any time points along the
probability flow ODE (PFODE) and score inference with a single function
evaluation, CTMs only allow translation from Gaussian noise to data. Thus, this
work aims to unlock the full potential of CTMs by proposing generalized CTMs
(GCTMs), which translate between arbitrary distributions via ODEs. We discuss
the design space of GCTMs and demonstrate their efficacy in various image
manipulation tasks such as image-to-image translation, restoration, and
editing. Code: \url{https://github.com/1202kbs/GCTM}
