---
title: "Latent Consistency Models — paper by Luo et al. (2023)"
description: "Latent diffusion models such as Stable Diffusion produce strong high-resolution text-to-image results. 35 references, cited by 99 papers here."
authors: ["Simian Luo", "Yiqin Tan", "Longbo Huang", "Jian Li", "Hang Zhao"]
year: 2023
venue: "arXiv:2310.04378"
source: "https://arxiv.org/abs/2310.04378"
doi: "10.48550/arxiv.2310.04378"
arxiv: "2310.04378"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/luo-2023-latent-consistency-models-synthesizing-high/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/luo-2023-latent-consistency-models-synthesizing-high/)

[home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2023](https://md.research.elamur.ai/free/en/papers/2023/page/6/) / Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference

# Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference

**Authors:** Simian Luo, Yiqin Tan, Longbo Huang, [Jian Li](https://md.research.elamur.ai/free/en/authors/jian-li/) and Hang Zhao · **Year:** 2023 · **Venue:** arXiv:2310.04378 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2310.04378) · [PDF](https://arxiv.org/pdf/2310.04378) · [DOI 10.48550/arxiv.2310.04378](https://doi.org/10.48550/arxiv.2310.04378) · [arXiv 2310.04378](https://arxiv.org/abs/2310.04378) · [OpenAlex](https://openalex.org/W4394656839)

**Citations:** 38 citations (OpenAlex, 2026-10-14) · [99](https://md.research.elamur.ai/free/en/papers/luo-2023-latent-consistency-models-synthesizing-high/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Latent diffusion models such as Stable Diffusion produce strong high-resolution text-to-image results. However, each image needs many sequential denoising passes, so generation is slow. The authors take Consistency Models, which had only been shown in pixel space on small benchmarks without text conditioning or guidance, and move them into the latent space of a pretrained Stable Diffusion autoencoder. The result is Latent Consistency Models (LCMs). They treat classifier-free guided sampling as an augmented PF-ODE. In a single distillation stage, the student learns to jump from any noisy latent directly to the end of its trajectory. A SKIPPING-STEP technique compares timesteps several steps apart to speed up convergence. Latent Consistency Fine-tuning (LCF) adapts a trained LCM to a custom image collection without losing fast sampling. Teachers are SD-V2.1 models, and training data are LAION-Aesthetics subsets. The models generate 768×768 images in 2–4 steps, or even one. The authors report state-of-the-art few-step quality on LAION-5B-Aesthetics and better results than a reproduced Guided-Distill at equal compute. A working model takes about 32 A100 GPU hours to distill, which makes fast sampling cheap to obtain.

## Key points
- A high-quality 768×768 LCM for 2–4-step sampling can be distilled from a pretrained Stable Diffusion checkpoint in about 4,000 training steps, roughly 32 A100 GPU hours. The demo figures use the Dreamer-V7 variant of SD.
- Two resolution settings are used:
  - **512×512:** teacher SD-V2.1-Base (ϵ-prediction), data LAION-Aesthetics-6+ (about 12M text-image pairs).
  - **768×768:** teacher SD-V2.1 (v-prediction), data LAION-Aesthetics-6.5+ (about 650K pairs).
- The main experiments run 100K iterations on 8 A100s with the following settings:
  - batch size 72 at 512 resolution and 16 at 768 resolution;
  - learning rate 8e-6, EMA rate 0.999943, Rectified Adam optimizer;
  - DDIM-Solver with skipping step k = 20;
  - guidance scale ω sampled from [2, 14].
- Guided-Distill (Meng et al., 2023) is not open-source, so the authors reimplemented its two-stage pipeline. They matched batch size and iteration budget to the LCM runs for a fair comparison. Under this equal budget, LCM converged faster and produced better results.
- Earlier Consistency Models were tested only on ImageNet 64×64 and LSUN 256×256. This work extends them to conditional, guided, high-resolution text-to-image generation.

## Interesting ideas
- **Guidance strength as a model input.** The guidance scale ω is fed to the network via a Fourier embedding whose projection is zero-initialized. This folds a two-pass inference trick into a single learned model. The same approach could suit any system with a tunable inference knob, such as temperature-like or mixing coefficients, and zero-init keeps the pretrained backbone stable when the new input is added.
- **Enforcing consistency across larger gaps.** The consistency loss compares points k steps apart instead of adjacent ones. Adjacent points carry a weak training signal, so the wider gap speeds learning. This is a general lesson for self-consistency or temporal-smoothness objectives: comparing nearly identical states teaches little.
- **Building the boundary condition into the parameterization.** The output mixes the input and the network prediction with time-dependent weights (c_skip, c_out), so the identity constraint at the trajectory start holds exactly. Hard-wiring a known constraint this way avoids spending capacity or loss terms on learning it.
- **Distilling inside an existing compressed space.** The student is trained in the frozen autoencoder latent space of the teacher rather than in raw pixels. This keeps distillation cheap and lets one recipe apply to many fine-tuned checkpoints of the same base. The pattern could transfer to other heavy models that already have a learned encoder.
- **Budget-matched baseline reproduction.** The authors reimplemented a closed baseline and matched batch size and iteration count to their own runs. They also openly note that the original baseline used more compute. This makes the comparison more honest and is a good template whenever a competitor's code is unavailable.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

📚 Shelves (3): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 18,614 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 17,965 works · [👁️ Computer Vision and Pattern Recognition](https://md.research.elamur.ai/free/en/shelves/computer-science/computer-vision-and-pattern-recognition/) · 3,486 works

## Cite

Cite as: Simian Luo, Yiqin Tan, Longbo Huang, Jian Li and Hang Zhao. 2023. Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference. arXiv:2310.04378.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{luo2023latent,
  title = {{Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference}},
  author = {Simian Luo, Yiqin Tan, Longbo Huang, Jian Li and Hang Zhao},
  year = {2023},
  doi = {10.48550/arxiv.2310.04378},
  eprint = {2310.04378},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2310.04378}
}
```

- [← previous Theory of Mind for Multi-Agent Collaboration via Large Language Models](https://md.research.elamur.ai/free/en/papers/li-2023-theory-mind-multi-agent-collaboration/)
- [next → Set-of-Mark Prompting Unleashes Extraordinary Visual Grounding in GPT-4V](https://md.research.elamur.ai/free/en/papers/yang-2023-set-mark-prompting-unleashes-extraordinary/)
- [↑ back to papers of 2023](https://md.research.elamur.ai/free/en/papers/2023/page/6/)

## References

35 references, 10 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pp. 248–255. [find](https://scholar.google.com/scholar?q=Jia+Deng%2C+Wei+Dong%2C+Richard+Socher%2C+Li%2DJia+Li%2C+Kai+Li%2C+and+Li+Fei%2DFei%2E+Imagenet%3A+A+large%2Dscale+hierarchical+image+database%2E+In+2009+IEEE+conference+on+computer+vision+and+pattern+recognition%2C+pp%2E+248%E2%80%93)
2. Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11):139–144, 2020. [find](https://scholar.google.com/scholar?q=Ian+Goodfellow%2C+Jean+Pouget%2DAbadie%2C+Mehdi+Mirza%2C+Bing+Xu%2C+David+Warde%2DFarley%2C+Sherjil+Ozair%2C+Aaron+Courville%2C+and+Yoshua+Bengio%2E+Generative+adversarial+networks%2E+Communications+of+the+ACM%2C+63%2811%29%3A139%E2%80%93)
3. Jonathan Ho and Tim Salimans. arXiv:2207.[12598, 2022](https://md.research.elamur.ai/free/en/papers/ho-2022-classifier-free-diffusion-guidance/).
4. Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840–6851, 2020. [find](https://scholar.google.com/scholar?q=Jonathan+Ho%2C+Ajay+Jain%2C+and+Pieter+Abbeel%2E+Denoising+diffusion+probabilistic+models%2E+Advances+in+Neural+Information+Processing+Systems%2C+33%3A6840%E2%80%936851%2C+2020%2E)
5. Aapo Hyvärinen and Peter Dayan. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research, 6(4), 2005. [find](https://scholar.google.com/scholar?q=Aapo+Hyva%CC%88rinen+and+Peter+Dayan%2E+Estimation+of+non%2Dnormalized+statistical+models+by+score+matching%2E+Journal+of+Machine+Learning+Research%2C+6%284%29%2C+2005%2E)
6. Alexia Jolicoeur-Martineau, Ke Li, Rémi Piché-Taillefer, Tal Kachman, and Ioannis Mitliagkas. Gotta go fast when generating data with score-based models. arXiv preprint arXiv:2105.14080, 2021. — [arXiv:2105.14080](https://arxiv.org/abs/2105.14080) [find](https://scholar.google.com/scholar?q=Alexia+Jolicoeur%2DMartineau%2C+Ke+Li%2C+Re%CC%81mi+Piche%CC%81%2DTaillefer%2C+Tal+Kachman%2C+and+Ioannis+Mitliagkas%2E+Gotta+go+fast+when+generating+data+with+score%2Dbased+models%2E+arXiv+preprint+arXiv%3A2105%2E14080%2C+2021%2E+%E2%80%94+%5Bar)
7. Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in Neural Information Processing Systems, 35:26565–26577, 2022. [find](https://scholar.google.com/scholar?q=Tero+Karras%2C+Miika+Aittala%2C+Timo+Aila%2C+and+Samuli+Laine%2E+Elucidating+the+design+space+of+diffusion%2Dbased+generative+models%2E+Advances+in+Neural+Information+Processing+Systems%2C+35%3A26565%E2%80%9326577%2C+2022%2E)
8. Diederik P Kingma and Max Welling. arXiv:1312.[6114, 2013](https://md.research.elamur.ai/free/en/papers/kingma-2013-auto-encoding-variational-bayes/).
9. Liyuan Liu, Haoming Jiang, Pengcheng He, Weizhu Chen, Xiaodong Liu, Jianfeng Gao, and Jiawei Han. On the variance of the adaptive learning rate and beyond. arXiv preprint arXiv:1908.03265, 2019. [find](https://scholar.google.com/scholar?q=Liyuan+Liu%2C+Haoming+Jiang%2C+Pengcheng+He%2C+Weizhu+Chen%2C+Xiaodong+Liu%2C+Jianfeng+Gao%2C+and+Jiawei+Han%2E+On+the+variance+of+the+adaptive+learning+rate+and+beyond%2E+arXiv+preprint+arXiv%3A1908%2E03265%2C+2019%2E)
10. Xingchao Liu, Chengyue Gong, and Qiang Liu. [Flow straight and fast: Learning to generate and transfer data with rectified flow](https://md.research.elamur.ai/free/en/papers/liu-2022-flow-straight-fast-learning-generate/). arXiv preprint arXiv:2209.03003, 2022.
11. Xingchao Liu, Xiwen Zhang, Jianzhu Ma, Jian Peng, and Qiang Liu. Instaflow: One step is enough for high-quality diffusion-based text-to-image generation. arXiv preprint arXiv:2309.06380, 2023. [find](https://scholar.google.com/scholar?q=Xingchao+Liu%2C+Xiwen+Zhang%2C+Jianzhu+Ma%2C+Jian+Peng%2C+and+Qiang+Liu%2E+Instaflow%3A+One+step+is+enough+for+high%2Dquality+diffusion%2Dbased+text%2Dto%2Dimage+generation%2E+arXiv+preprint+arXiv%3A2309%2E06380%2C+2023%2E)
12. Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. arXiv preprint arXiv:2206.00927, 2022a. [find](https://scholar.google.com/scholar?q=Cheng+Lu%2C+Yuhao+Zhou%2C+Fan+Bao%2C+Jianfei+Chen%2C+Chongxuan+Li%2C+and+Jun+Zhu%2E+Dpm%2Dsolver%3A+A+fast+ode+solver+for+diffusion+probabilistic+model+sampling+in+around+10+steps%2E+arXiv+preprint+arXiv%3A2206%2E00927%2C+20)
13. Origin LCM 1K Finetuning 10K Finetuning 30K Finetuning Classifier-free diffusion guidance. arXiv preprint Auto-encoding variational bayes. arXiv preprint Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic m… — [arXiv:2211.01095](https://arxiv.org/abs/2211.01095) [find](https://scholar.google.com/scholar?q=Origin+LCM+1K+Finetuning+10K+Finetuning+30K+Finetuning+Classifier%2Dfree+diffusion+guidance%2E+arXiv+preprint+Auto%2Dencoding+variational+bayes%2E+arXiv+preprint+Cheng+Lu%2C+Yuhao+Zhou%2C+Fan+Bao%2C+Jianfei+Chen%2C+C)
14. Zhaoyang Lyu, Xudong Xu, Ceyuan Yang, Dahua Lin, and Bo Dai. Accelerating diffusion models via early stop of the diffusion process. arXiv preprint arXiv:2205.12524, 2022. — [arXiv:2205.12524](https://arxiv.org/abs/2205.12524) [find](https://scholar.google.com/scholar?q=Zhaoyang+Lyu%2C+Xudong+Xu%2C+Ceyuan+Yang%2C+Dahua+Lin%2C+and+Bo+Dai%2E+Accelerating+diffusion+models+via+early+stop+of+the+diffusion+process%2E+arXiv+preprint+arXiv%3A2205%2E12524%2C+2022%2E+%E2%80%94+%5BarXiv%3A2205%2E12524%5D%28https%3A%2F%2F)
15. Chenlin Meng, Robin Rombach, Ruiqi Gao, Diederik Kingma, Stefano Ermon, Jonathan Ho, and Tim Salimans. On distillation of guided diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 14297–14306, 2023. [find](https://scholar.google.com/scholar?q=Chenlin+Meng%2C+Robin+Rombach%2C+Ruiqi+Gao%2C+Diederik+Kingma%2C+Stefano+Ermon%2C+Jonathan+Ho%2C+and+Tim+Salimans%2E+On+distillation+of+guided+diffusion+models%2E+In+Proceedings+of+the+IEEE%2FCVF+Conference+on+Computer)
16. Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, Ilya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. arXiv preprint arXiv:2112.10741, 2021. [find](https://scholar.google.com/scholar?q=Alex+Nichol%2C+Prafulla+Dhariwal%2C+Aditya+Ramesh%2C+Pranav+Shyam%2C+Pamela+Mishkin%2C+Bob+McGrew%2C+Ilya+Sutskever%2C+and+Mark+Chen%2E+Glide%3A+Towards+photorealistic+image+generation+and+editing+with+text%2Dguided+diff)
17. Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, pp. 8162–8171. PMLR, 2021. [find](https://scholar.google.com/scholar?q=Alexander+Quinn+Nichol+and+Prafulla+Dhariwal%2E+Improved+denoising+diffusion+probabilistic+models%2E+In+International+Conference+on+Machine+Learning%2C+pp%2E+8162%E2%80%938171%2E+PMLR%2C+2021%2E)
18. Norod78. Simpsons blip captions. [https://huggingface.co/datasets/Norod78/simpsons-blip-captions](https://huggingface.co/datasets/Norod78/simpsons-blip-captions), 2022. [↗](https://huggingface.co/datasets/Norod78/simpsons-blip-captions)
19. Justin N. M. Pinkney. Pokemon blip captions. [https://huggingface.co/datasets/lambdalabs/pokemon-blip-captions/](https://huggingface.co/datasets/lambdalabs/pokemon-blip-captions/), 2022. [↗](https://huggingface.co/datasets/lambdalabs/pokemon-blip-captions/)
20. Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. [Hierarchical text-conditional image generation with clip latents](https://md.research.elamur.ai/free/en/papers/ramesh-2022-hierarchical-text-conditional-image-generation/). arXiv preprint arXiv:2204.06125, 2022.
21. Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. [High-resolution image synthesis with latent diffusion models](https://md.research.elamur.ai/free/en/papers/rombach-2021-high-resolution-image-synthesis-latent/). In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10684–10695, 2022.
22. Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. [Photorealistic text-to-image diffusion models with deep language understanding](https://md.research.elamur.ai/free/en/papers/saharia-2022-photorealistic-text-image-diffusion-models/). Advances in Neural Information Processing Systems, 35…
23. Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. arXiv preprint arXiv:2202.00512, 2022. — [arXiv:2202.00512](https://arxiv.org/abs/2202.00512) [find](https://scholar.google.com/scholar?q=Tim+Salimans+and+Jonathan+Ho%2E+Progressive+distillation+for+fast+sampling+of+diffusion+models%2E+arXiv+preprint+arXiv%3A2202%2E00512%2C+2022%2E+%E2%80%94+%5BarXiv%3A2202%2E00512%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2202%2E00512%29)
24. Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. [Laion-5b: An open large-scale dataset for training next generation image-text models](https://md.research.elamur.ai/free/en/papers/schuhmann-2022-laion-5b-open-large-scale/). arXiv preprint arXiv:2210.08402, 2022.
25. Kihyuk Sohn, Honglak Lee, and Xinchen Yan. Learning structured output representation using deep conditional generative models. Advances in neural information processing systems, 28, 2015. [find](https://scholar.google.com/scholar?q=Kihyuk+Sohn%2C+Honglak+Lee%2C+and+Xinchen+Yan%2E+Learning+structured+output+representation+using+deep+conditional+generative+models%2E+Advances+in+neural+information+processing+systems%2C+28%2C+2015%2E)
26. Jiaming Song, Chenlin Meng, and Stefano Ermon. [Denoising diffusion implicit models](https://md.research.elamur.ai/free/en/papers/song-2020-denoising-diffusion-implicit-models/). arXiv preprint arXiv:2010.02502, 2020a.
27. Yang Song and Stefano Ermon. [Generative modeling by estimating gradients of the data distribution](https://md.research.elamur.ai/free/en/papers/song-2019-generative-modeling-estimating-gradients-data/). Advances in Neural Information Processing Systems, 32, 2019.
28. Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. [Score-based generative modeling through stochastic differential equations](https://md.research.elamur.ai/free/en/papers/song-2020-score-based-generative-modeling-through/). arXiv preprint arXiv:2011.13456, 2020b.
29. Yang Song, Conor Durkan, Iain Murray, and Stefano Ermon. Maximum likelihood training of score-based diffusion models. Advances in Neural Information Processing Systems, 34:1415–1428, 2021. [find](https://scholar.google.com/scholar?q=Yang+Song%2C+Conor+Durkan%2C+Iain+Murray%2C+and+Stefano+Ermon%2E+Maximum+likelihood+training+of+score%2Dbased+diffusion+models%2E+Advances+in+Neural+Information+Processing+Systems%2C+34%3A1415%E2%80%931428%2C+2021%2E)
30. Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. arXiv preprint arXiv:2303.01469, 2023. [find](https://scholar.google.com/scholar?q=Yang+Song%2C+Prafulla+Dhariwal%2C+Mark+Chen%2C+and+Ilya+Sutskever%2E+Consistency+models%2E+arXiv+preprint+arXiv%3A2303%2E01469%2C+2023%2E)
31. Daniel Watson, Jonathan Ho, Mohammad Norouzi, and William Chan. Learning to efficiently sample from diffusion probabilistic models. arXiv preprint arXiv:2106.03802, 2021. — [arXiv:2106.03802](https://arxiv.org/abs/2106.03802) [find](https://scholar.google.com/scholar?q=Daniel+Watson%2C+Jonathan+Ho%2C+Mohammad+Norouzi%2C+and+William+Chan%2E+Learning+to+efficiently+sample+from+diffusion+probabilistic+models%2E+arXiv+preprint+arXiv%3A2106%2E03802%2C+2021%2E+%E2%80%94+%5BarXiv%3A2106%2E03802%5D%28https%3A%2F%2F)
32. Fisher Yu, Ari Seff, Yinda Zhang, Shuran Song, Thomas Funkhouser, and Jianxiong Xiao. Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. — [arXiv:1506.03365](https://arxiv.org/abs/1506.03365) [find](https://scholar.google.com/scholar?q=Fisher+Yu%2C+Ari+Seff%2C+Yinda+Zhang%2C+Shuran+Song%2C+Thomas+Funkhouser%2C+and+Jianxiong+Xiao%2E+Lsun%3A+Construction+of+a+large%2Dscale+image+dataset+using+deep+learning+with+humans+in+the+loop%2E+arXiv+preprint+arXi)
33. Lvmin Zhang and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. arXiv preprint arXiv:2302.05543, 2023. [find](https://scholar.google.com/scholar?q=Lvmin+Zhang+and+Maneesh+Agrawala%2E+Adding+conditional+control+to+text%2Dto%2Dimage+diffusion+models%2E+arXiv+preprint+arXiv%3A2302%2E05543%2C+2023%2E)
34. Hongkai Zheng, Weili Nie, Arash Vahdat, Kamyar Azizzadenesheli, and Anima Anandkumar. Fast sampling of diffusion models via operator learning. In International Conference on Machine Learning, pp. 42390–42402. PMLR, 2023. [find](https://scholar.google.com/scholar?q=Hongkai+Zheng%2C+Weili+Nie%2C+Arash+Vahdat%2C+Kamyar+Azizzadenesheli%2C+and+Anima+Anandkumar%2E+Fast+sampling+of+diffusion+models+via+operator+learning%2E+In+International+Conference+on+Machine+Learning%2C+pp%2E+4239)
35. Huangjie Zheng, Pengcheng He, Weizhu Chen, and Mingyuan Zhou. Truncated diffusion probabilistic models. stat, 1050:7, 2022. [find](https://scholar.google.com/scholar?q=Huangjie+Zheng%2C+Pengcheng+He%2C+Weizhu+Chen%2C+and+Mingyuan+Zhou%2E+Truncated+diffusion+probabilistic+models%2E+stat%2C+1050%3A7%2C+2022%2E)

*Updated 2 November 2026*
