Stable Continuous-Time Consistency Distillation: An Empirical Study with a Multistep Extension

Continuous-time consistency models are an attractive route to few-step generation. They remove the discretization error inherent to the timestep grid that discrete-time consistency models depend on. Until recently, however, training them was unstable. Lu & Song (2025) address this with the TrigFlow formulation and a coordinated set of architectural and training-objective changes. We conduct an independent empirical study of this framework on CIFAR-10 and ImageNet-64. No open-weight TrigFlow teachers exist at these scales, so we train them from scratch and then verify the consistency distillation (sCD) and consistency training (sCT) behavior of students initialized from these teachers. On CIFAR-10, our students reproduce the reported FID at one and two steps. On ImageNet-64, they fall short, a gap that appears related to our teacher and to architectural choices the paper leaves unspecified. We also report a parameter-count gap of about 5% between the model size stated in the paper and a faithful re-implementation, which we attribute to the scale-and-shift conditioning projections in Adaptive Double Normalization. We then propose Multistep sCD (MS-sCD), a continuous-time, segment-conditioned multistep generalization of sCD. The segment-conditioning idea is borrowed from the discrete-time multistep consistency distillation of Heek et al. (2024); we build on their preliminary continuous-time experiments within the TrigFlow/sCM framework. The rest of the algorithm follows sCD. MS-sCD replaces sCM's two-step intermediate time with a fixed segment-boundary schedule and recovers sCD at M = 1. We report FID at M = 2, 4, 8 and compare against the discrete-time MSCD baseline. Code, model weights, and training scripts are available on GitHub (Mathew et al., 2026).