reviews: 
Comments: The paper presents a unified perspective on diffusion-based and flow-based generative models and introduces a comprehensive set of techniques aimed at improving the training stability and overall performance of continuous-time consistency models for large-scale image generation. The techniques include: 1) enhancing time transformation and embeddings, 2) replacing the AdaGN layer with Adaptive Double Normalization, 3) normalizing the tangent function and applying tangent warm-up, 4) implementing an adaptive weighting function in the training objective, and 5) optimizing forward-mode differentiation. These techniques mitigate the numerical instability issues in continuous-time consistency models and enable the model to achieve highly competitive performance in class-conditioned image generation.
Strengths: S1 - The paper provides a comprehensive analysis and set of solutions addressing the numerical instability issues in continuous-time consistency models, significantly improving performance and enabling the model to achieve competitive results on selected benchmarks.

S2 - Many of the enhancements are supported by detailed theoretical justification and experimental results.

S3 - The unified perspective on previous diffusion and flow-matching parameterizations is thorough, complete, and well-grounded, offering novel insights that could benefit the community.

S4 - The paper is well-structured and easy to follow.
Weaknesses: W1 - Several design choices appear arbitrary and lack supporting evidence. 

For example, in Section 4.1, the authors discuss the preference for Adaptive Double Normalization over AdaGN, but there is no experimental evidence supporting this choice. It would be more insightful to add a Figure similar to Figure 5 show experimental comparison between Adaptive Double Norm and AdaGN. 

Similarly, in Section 4.2, the authors propose training with linear warm-up w.r.t the model's time derivative, yet no evidence is provided to demonstrate this choice’s effectiveness. Again, including an ablation study or comparative analysis showing the impact of the linear warm-up on training stability or performance metrics would provide more concrete evidence for the effectiveness of this specific choice

Furthermore, Figure 5(b) suggests that incorporating adaptive weighting in a two-step setting may lead to worse performance, while in the one-step setting, it only yields marginal improvement. Have the authors considered alternative designs for the two step case?

W2 - In Sections 4.1 and 5.2, the paper discusses the training compute of sCM. However, including a comparison of compute efficiency with other models (e.g., ECT [1]) would be more insightful, maybe a table or figure comparing the compute efficiency (e.g., FLOPs or training time) of sCM against ECT and other relevant baselines for a given performance level. 

Additionally, given that the model is trained on a large-scale dataset (ImageNet 512) under latent setting, it would be beneficial to include discussions related to text-to-image generation.

[1] Geng, Zhengyang, Ashwini Pokle, William Luo, Justin Lin, and J. Zico Kolter. "Consistency Models Made Easy." arXiv preprint arXiv:2406.14548 (2024).
Recommendation: 8
Reviewer confidence: 3
Soundness/correctness: 3
Clarity: 4