# Binxu Wang ## Analytical Theory of Spectral Bias in Diffusion [ Analytical Theory of Spectral Bias in Diffusion arrow\_circle\_right ](https://arxiv.org/abs/2503.03206) ![SpectralBias_Schematics](/sites/g/files/omnuum11221/files/styles/hwp_28_10__1920x685/public/binxuw/files/figure_schematics_spectralbias.png?itok=uE0Rwpgx) ![binxu_portrait](/sites/g/files/omnuum11221/files/styles/hwp_1_1__720x720_scale/public/binxuw/files/20201029_ponce_5d_0080_2.jpg?itok=xVuoIWK6) I have the honor of being among the inaugural NeuroAI [Research Fellows](https://www.harvard.edu/kempner-institute/opportunities/the-kempner-institute-postdoctoral-fellowship/) at the newly established [Kempner Institute for the Study of Natural and Artificial Intelligence](https://www.harvard.edu/kempner-institute/) at Harvard University, where I started in fall 2023. I obtained my Ph.D. degree in Neuroscience in August 2023. I was fortunate to be advised by Dr. [Carlos Ponce](https://ponce.hms.harvard.edu/) from Harvard's Neurobiology Department. I started my Ph.D. journey in the [neuroscience program](https://neuroscience.wustl.edu/) at Washington University in St. Louis. In fall 2021, I moved with the Ponce lab to Harvard Medical School. I'm interested in using optimization, generative models and geometry to understand the representation of visual information in the primate brain and deep neural networks. I hope computation and theory combined with experiments in close-loop will bring us closer to understand the brain. My [bio sketch.](/bio) See also: [Google Scholar](https://scholar.google.com/citations?user=8-njUc8AAAAJ) / [GitHub](https://github.com/Animadversio) / [Twitter](https://twitter.com/WangBinxu) / [Personal Blog](https://animadversio.github.io/) / [YouTube](https://www.youtube.com/@binxuwang4960) ## Latest News [### I gave a talk at Spring into Science retreat! on Analytical Theory of Spectral Bias in Diffusion Sampling and Learning ](/news/i-gave-talk-spring-science-retreat-analytical-theory-spectral-bias-diffusion-sampling) March 26, 2025 [### I gave a Special Seminar at Neuroscience Department in Washington University in St Louis! ](/news/giving-special-seminar-neuroscience-department-washington-university-st-louis) February 18, 2025 [### I gave a talk in Cognitive & Neural Computation Lab at Yale! ](/news/giving-talk-alignment-neural-representation-and-generative-models-cognitive-neural) February 12, 2025 [### I gave a talk in Nanosymposium at SfN2024, Chicago! ](/news/i-gave-talk-nanosymposium-sfn2024-chicago) October 08, 2024 [### I gave a talk at NAISYS2024, Cold Spring Harbour! ](/news/i-gave-talk-alignment-neural-code-and-generative-models-naisys2024-cold-spring-harbour) September 28, 2024 [### Attending KITP DL2023, Program in Deep Learning from the Perspective of Physics and Neuroscience, at Santa Barbara ](/news/attending-kitp-dl2023-program-deep-learning-perspective-physics-and-neuroscience-santa) November 26, 2023 [### I gave a talk at Nanosymbosium at SfN2023, DC! ](/news/i-gave-talk-nanosymbosium-sfn2023-dc) November 10, 2023 [### I successfully defended my PhD thesis! ](/news/i-successfully-defended-my-phd-thesis) August 23, 2023 [ More arrow\_circle\_right ](/news) ## Recent Publications Download 6 citations download- [BibTeX](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=bibtex) - [EndNote X3 XML](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=endnote8) - [EndNote 7 XML](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=endnote7) - [Endnote tagged](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=tagged) - [Marc](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=marc) - [PubMedId](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=pubmed_id) - [RIS](/bibcite/export?pager_style=no_pager&number_of_items=6&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=ris) ### Working Paper Binxu Wang and John Vastola. “[Diffusion Models Generate Images Like Painters: An Analytical Theory of Outline First, Details Later](/publications/diffusion-models-generate-images-painters-analytical-theory-outline-first)” Binxu Wang and John Vastola. “[Diffusion Models Generate Images Like Painters: An Analytical Theory of Outline First, Details Later](/publications/diffusion-models-generate-images-painters-analytical-theory-outline-first)” - add\_circle do\_not\_disturb\_on Abstract - [ descriptionPublisher's Version](https://arxiv.org/abs/2303.02490) How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image... - [ descriptionPublisher's Version](https://arxiv.org/abs/2303.02490) ### Submitted Binxu Wang. “[An Analytical Theory of Power Law Spectral Bias in the Learning Dynamics of Diffusion Models](https://arxiv.org/abs/2503.03206)”. ArXiv Preprint ArXiv:2503.03206 Binxu Wang. “[An Analytical Theory of Power Law Spectral Bias in the Learning Dynamics of Diffusion Models](https://arxiv.org/abs/2503.03206)”. ArXiv Preprint ArXiv:2503.03206 - add\_circle do\_not\_disturb\_on Abstract - [ descriptionPublisher's Version](https://arxiv.org/abs/2503.03206) We developed an analytical framework for understanding how the learned distribution evolves during diffusion model training. Leveraging the Gaussian equivalence principle, we derived exact solutions for the gradient-flow dynamics of weights in one- or two... - [ descriptionPublisher's Version](https://arxiv.org/abs/2503.03206) Binxu Wang and Carlos Ponce. “[Neural Dynamics of Object Manifold Alignment in the Ventral Stream](https://www.biorxiv.org/content/10.1101/2024.06.20.596072v1)”. BioRxiv, Pp. 2024–06 Binxu Wang and Carlos Ponce. “[Neural Dynamics of Object Manifold Alignment in the Ventral Stream](https://www.biorxiv.org/content/10.1101/2024.06.20.596072v1)”. BioRxiv, Pp. 2024–06 - add\_circle do\_not\_disturb\_on Abstract - [ descriptionPublisher's Version](https://www.biorxiv.org/content/10.1101/2024.06.20.596072v1) Visual neurons respond across a vast landscape of images, comprising objects, textures, and places. Natural images can be parameterized using deep generative networks, raising the question of whether latent factors learned by some networks control images... - [ descriptionPublisher's Version](https://www.biorxiv.org/content/10.1101/2024.06.20.596072v1) ### 2024 Binxu Wang, Jiaqi Shang, and Haim Sompolinsky. 2024. “[Do Diffusion Models Generalize on Abstract Rules for Reasoning?](/publications/do-diffusion-models-generalize-abstract-rules-reasoning)”. In 2024 Conference on Cognitive Computational Neuroscience Binxu Wang, Jiaqi Shang, and Haim Sompolinsky. 2024. “[Do Diffusion Models Generalize on Abstract Rules for Reasoning?](/publications/do-diffusion-models-generalize-abstract-rules-reasoning)”. In 2024 Conference on Cognitive Computational Neuroscience Binxu Wang, Jiaqi Shang, and Haim Sompolinsky. 2024. “[Diverse Capability and Scaling of Diffusion and Auto-Regressive Models When Learning Abstract Rules](https://arxiv.org/abs/2411.07873)”. In The First Workshop on System-2 Reasoning at Scale, NeurIPS’24 Binxu Wang, Jiaqi Shang, and Haim Sompolinsky. 2024. “[Diverse Capability and Scaling of Diffusion and Auto-Regressive Models When Learning Abstract Rules](https://arxiv.org/abs/2411.07873)”. In The First Workshop on System-2 Reasoning at Scale, NeurIPS’24 - add\_circle do\_not\_disturb\_on Abstract - [ descriptionPublisher's Version](https://arxiv.org/abs/2411.07873) Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform reasoning through... - [ descriptionPublisher's Version](https://arxiv.org/abs/2411.07873) Binxu Wang and John Vastola. 2024. “[The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and Its Applications](https://arxiv.org/abs/2412.09726)”. Transactions on Machine Learning Research Binxu Wang and John Vastola. 2024. “[The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and Its Applications](https://arxiv.org/abs/2412.09726)”. Transactions on Machine Learning Research - add\_circle do\_not\_disturb\_on Abstract - [ descriptionPublisher's Version](https://openreview.net/forum?id=I0uknSHM2j) By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of... - [ descriptionPublisher's Version](https://openreview.net/forum?id=I0uknSHM2j) [ More arrow\_circle\_right ](/publications)