reviews: 
Comments: This paper investigates a fundamental topic in consistency models (CMs), specifically the challenges of discretization errors and the resulting training stability issue. Consistency Models can be trained in discrete or continuous time, either from scratch using a dataset or distilled from pretrained teacher scores. CMs' theoretical foundation elucidates the importance of controlling the discretization error and eventually achieving consistency in continuous time. While continuous-time CMs eliminate the discretization errors present in their discrete-time counterparts, they suffer from training instability, a problem that is not yet well understood in the research community.

This work conducts a comprehensive study into continuous-time CMs, covering forward process parameterization, network architecture, and training techniques. The authors first develop a simplified diffusion process formulation called TrigFlow, which unifies EDM and Flow Matching for the first time. Building upon this foundation, they analyze the gradient flow of continuous-time CMs, identify the root cause of training instability, and mitigate this issue through modifications to time embeddings and adaptive group normalization. Additional training techniques, such as adaptive weighting functions and annealing, further contribute to improved training stability and scalability.

The resulting method, sCT/sCD, allows continuous-time CMs to be trained at an unprecedented scale, scaling up to 1.5B parameters on ImageNet 512x512. These results significantly narrow the performance gap between CMs and state-of-the-art diffusion models to less than 10% in FID, while matching or even surpassing adversarial methods and discrete/continuous autoregressive models in both performance and efficiency.
Strengths: This is a very strong paper in analysis, practical techniques, writing, and experiment results. 

- Novelty. This paper's novelty is evident in several aspects.
    - First, it studies an important but less studied problem: consistency models in continuous time, together with the training stability and discretization error of consistency models. 
    - The proposed TrigFlow, as a novel unification of EDM and Flow Matching, substantially simplifies the analysis presented later and the practical techniques.
    - The gradient analysis of continuous-time objective reveals the root cause of instability. To the best of my knowledge, this is the first paper to establish the gradient analysis for CMs.
    - Model architecture modifications are original since existing works are mostly inherited from Diffusion Models' design and focus on the training techniques and formulations, leaving the architectural design underexplored.

- Soundness. Its technical claims are well backed up by both theoretical analysis and empirical results. I particularly appreciate the in-depth investigation into the training dynamics and gradient analysis of continuous-time CMs.

- Presentation. The logical flow of this paper is well structured and smooth. The problem statement is clearly defined, and the explanation of why discretization errors matter for CMs and the motivation toward continuous-time formulation is crystal clear. The gradient analysis into continuous-time CMs is thoughtfully motivated and carefully organized. Even the appendix is well-written, offering useful insights into the proposed techniques.

- Experiments. Proposed techniques allow for training continuous-time Consistency Models (sCMs) at an unprecedented scale. Experiment results are impressive, matching/outperforming adversarial approaches, score distillation, and recent autoregressive models.
    - Gradient variances have been carefully controlled via adaptive weighting and normalization techniques.
    - Comprehensively studying the scaling behaviors of sCMs under continuous-time training. 
    - Comparisons with improved score distillation baseline using many methods developed in this work confirm the mode coverage of CMs.
    - Additionally, the paper discusses efficient and stable implementation strategies for continuous-time CMs.

Given the potential impact of this paper, I strongly recommend acceptance with conference highlights. It was a great pleasure to read through the manuscript!
Weaknesses: I did not find any apparent weaknesses in the analysis or experiments (including both ablation studies and performance evaluation). There are research questions worth further investigation, as discussed below.
Recommendation: 10
Reviewer confidence: 5
Soundness/correctness: 4
Clarity: 3