Generalized Consistency Trajectory Models (GCTMs) builds upon the foundation laid by Consistency Trajectory Models (CTMs), introducing a new capability: the ability to seamlessly translate between arbitrary distributions with just a single step. This breakthrough marks a departure from the constraints of traditional CTMs, which were limited to transforming Gaussian noise to data. By harnessing the power of Conditional Flow Matching Theory, GCTMs transcend these limitations, enabling practitioners to navigate a diverse array of distribution landscapes with unparalleled ease.

GCTMs boasts its capacity to learn and traverse the Flow Matching Ordinary Differential Equation (ODE), a mathematical construct capable of interpolating between two arbitrary distributions. Unlike their predecessors, GCTMs embrace a spectrum of possibilities, offering practitioners the flexibility to choose couplings that suit both unsupervised and supervised settings. This adaptability accelerates the deployment of zero-shot and supervised image manipulation algorithms, unlocking new avenues for creativity and innovation.