Part 8 · The Papers & Sources

The complete reference list

1. Inception Labs, “About” — inceptionlabs.ai/about (accessed 2026-08-01). The primary source: the nine-paper list and the Mercury claims.
2. Jiaming Song, Chenlin Meng, Stefano Ermon (2020). Denoising Diffusion Implicit Models. ICLR 2021. arXiv:2010.02502.
3. Lili Chen, Kevin Lu, Aravind Rajeswaran, Kimin Lee, Aditya Grover, Michael Laskin, Pieter Abbeel, Aravind Srinivas, Igor Mordatch (2021). Decision Transformer: Reinforcement Learning via Sequence Modeling. NeurIPS 2021. arXiv:2106.01345.
4. Tri Dao, Daniel Y. Fu, Stefano Ermon, Atri Rudra, Christopher Ré (2022). FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness. NeurIPS 2022. arXiv:2205.14135.
5. Rafael Rafailov, Archit Sharma, Eric Mitchell, Stefano Ermon, Christopher D. Manning, Chelsea Finn (2023). Direct Preference Optimization: Your Language Model is Secretly a Reward Model. NeurIPS 2023. arXiv:2305.18290.
6. Subham Sekhar Sahoo, Marianne Arriola, Yair Schiff, Aaron Gokaslan, Edgar Marroquin, Justin T. Chiu, Alexander Rush, Volodymyr Kuleshov (2024). Simple and Effective Masked Diffusion Language Models. NeurIPS 2024. arXiv:2406.07524.
7. Yair Schiff, Subham Sekhar Sahoo, Hao Phung, Guanghan Wang, Sam Boshar, Hugo Dalla-torre, Bernardo P. de Almeida, Alexander Rush, Thomas Pierrot, Volodymyr Kuleshov (2024). Simple Guidance Mechanisms for Discrete Diffusion Models. ICLR 2025. arXiv:2412.10193.
8. Marianne Arriola, Aaron Gokaslan, Justin T. Chiu, Zhihan Yang, Zhixuan Qi, Jiaqi Han, Subham Sekhar Sahoo, Volodymyr Kuleshov (2025). Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models. ICLR 2025. arXiv:2503.09573.
9. Guanghan Wang, Yair Schiff, Subham Sekhar Sahoo, Volodymyr Kuleshov (2025). Remasking Discrete Diffusion Models (project page, as linked by the primary source). arXiv preprint, 2025.
10. Siyan Zhao, Devaansh Gupta, Qinqing Zheng, Aditya Grover (2025). d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning. arXiv preprint, 2025.
11. Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, Surya Ganguli (2015). Deep Unsupervised Learning using Nonequilibrium Thermodynamics. ICML 2015. The origin of the diffusion idea.
12. Jonathan Ho, Ajay Jain, Pieter Abbeel (2020). Denoising Diffusion Probabilistic Models. NeurIPS 2020. The forward process, posterior, and L_simple of Maths I.
13. Yang Song, Stefano Ermon (2019). Generative Modeling by Estimating Gradients of the Data Distribution. NeurIPS 2019. The score-based view.
14. Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole (2020). Score-Based Generative Modeling through Stochastic Differential Equations. ICLR 2021. The SDE unification in the score callout.
15. Jacob Austin, Daniel D. Johnson, Jonathan Ho, Daniel Tarlow, Rianne van den Berg (2021). Structured Denoising Diffusion Models in Discrete State-Spaces (D3PM). NeurIPS 2021. The general discrete framework; masking is its absorbing-state case.
16. Jacob Devlin, Ming-Wei Chang, Kenton Lee, Kristina Toutanova (2018). BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. NAACL 2019. The MLM loss that MDLM integrates.
17. Jonathan Ho, Tim Salimans (2022). Classifier-Free Diffusion Guidance. The mechanism ported to discrete diffusion; a quiz reference.
18. Tim Salimans, Jonathan Ho (2022). Progressive Distillation for Fast Sampling of Diffusion Models. ICLR 2022. The other route to fewer steps; a quiz distractor.
19. Alex Nichol, Prafulla Dhariwal (2021). Improved Denoising Diffusion Probabilistic Models. ICML 2021. Schedule learning; a quiz distractor.
20. Diederik P. Kingma, Tim Salimans, Ben Poole, Jonathan Ho (2021). Variational Diffusion Models. NeurIPS 2021. Likelihood-focused training; a quiz distractor.
21. William Peebles, Saining Xie (2022). Scalable Diffusion Models with Transformers (DiT). ICCV 2023. Architecture as the other speed axis; a quiz distractor.
22. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, Y.K. Li, Y. Wu, Daya Guo (2024). DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models. The GRPO that diffu-GRPO adapts.
23. Shen Nie, Fengqi Zhu, Zebin You, Xiaolu Zhang, Jingyang Ou, Jun Hu, Jun Zhou, Yankai Lin, Ji-Rong Wen, Chongxuan Li (2025). Large Language Diffusion Models (LLaDA). The pretrained dLLM d1 builds on.

Suggested reading order if you want to go to the sources: skim MDLM first (its intro is the best short statement of the whole field, and Maths II is your map of its notation), then Block Diffusion and ReMDM for the two big fixes (Maths III has their equations), d1 for where this is headed, and keep DDIM for when you want the image-diffusion roots in full mathematical dress.