Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme

Ruofeng Yang, Bo Jiang, Cheng Chen, Shuai Li
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:70756-70775, 2025.

Abstract

Consistency models, a new class of one-step generative models, have shown competitive performance with multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the continuous diffusion process into $K$ steps and trains a one-step mapping function on these discretized timepoints. Despite the empirical success, only a few works focus on the discretization complexity $K$, and their setting is far from that of empirical works. More specifically, the current theoretical works analyze the variance preserving (VP) diffusion process with a uniform stepsize, while empirical works adopt a variance exploding (VE) process with a decay discretization stepsize. As a result, these works suffer from large discretization complexity and fail to explain the empirical success of consistency models. To close the gap between theory and application, we analyze consistency models with (1) VE process and (2) decay stepsize and prove the state-of-the-art discretization complexity for consistency models. This result is competitive with the results of diffusion models and shows the potential of consistency models. To balance the computation and performance, previous empirical work further proposes a $2$-step consistency algorithm. In this work, we also analyze the role of $2$-step sampling and show that it improves the discretization complexity compared with one-step generation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-yang25l, title = {Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme}, author = {Yang, Ruofeng and Jiang, Bo and Chen, Cheng and Li, Shuai}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {70756--70775}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/yang25l/yang25l.pdf}, url = {https://proceedings.mlr.press/v267/yang25l.html}, abstract = {Consistency models, a new class of one-step generative models, have shown competitive performance with multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the continuous diffusion process into $K$ steps and trains a one-step mapping function on these discretized timepoints. Despite the empirical success, only a few works focus on the discretization complexity $K$, and their setting is far from that of empirical works. More specifically, the current theoretical works analyze the variance preserving (VP) diffusion process with a uniform stepsize, while empirical works adopt a variance exploding (VE) process with a decay discretization stepsize. As a result, these works suffer from large discretization complexity and fail to explain the empirical success of consistency models. To close the gap between theory and application, we analyze consistency models with (1) VE process and (2) decay stepsize and prove the state-of-the-art discretization complexity for consistency models. This result is competitive with the results of diffusion models and shows the potential of consistency models. To balance the computation and performance, previous empirical work further proposes a $2$-step consistency algorithm. In this work, we also analyze the role of $2$-step sampling and show that it improves the discretization complexity compared with one-step generation.} }
Endnote
%0 Conference Paper %T Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme %A Ruofeng Yang %A Bo Jiang %A Cheng Chen %A Shuai Li %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-yang25l %I PMLR %P 70756--70775 %U https://proceedings.mlr.press/v267/yang25l.html %V 267 %X Consistency models, a new class of one-step generative models, have shown competitive performance with multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the continuous diffusion process into $K$ steps and trains a one-step mapping function on these discretized timepoints. Despite the empirical success, only a few works focus on the discretization complexity $K$, and their setting is far from that of empirical works. More specifically, the current theoretical works analyze the variance preserving (VP) diffusion process with a uniform stepsize, while empirical works adopt a variance exploding (VE) process with a decay discretization stepsize. As a result, these works suffer from large discretization complexity and fail to explain the empirical success of consistency models. To close the gap between theory and application, we analyze consistency models with (1) VE process and (2) decay stepsize and prove the state-of-the-art discretization complexity for consistency models. This result is competitive with the results of diffusion models and shows the potential of consistency models. To balance the computation and performance, previous empirical work further proposes a $2$-step consistency algorithm. In this work, we also analyze the role of $2$-step sampling and show that it improves the discretization complexity compared with one-step generation.
APA
Yang, R., Jiang, B., Chen, C. & Li, S.. (2025). Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:70756-70775 Available from https://proceedings.mlr.press/v267/yang25l.html.

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