{ "148881-21905043": { "datetime_modified":"20261009T150233", "datetime_start":"20261106T150000", "datetime_end":"20261106T160000", "has_end_time":1, "date_start":"2026-11-06", "date_end":"2026-11-06", "time_start":"15:00:00", "time_end":"16:00:00", "time_zone":"America\/Detroit", "event_title":"AIM Seminar: The Geometry of Diffusion Generation: A Log-Density Ridge Perspective", "occurrence_title":"", "combined_title":"AIM Seminar: The Geometry of Diffusion Generation: A Log-Density Ridge Perspective: Ye He (Applied Mathematics, University of Colorado Boulder)", "event_subtitle":"Ye He (Applied Mathematics, University of Colorado Boulder)", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"Abstract: Diffusion models generate data by gradually transforming noise into structured samples. When these samples differ from the training examples, what determines their geometric organization? In this talk, I will present a framework based on log-density ridges of the smoothed empirical distribution. These evolving structures provide a geometric reference for analyzing generation relative to a finite training set. I will describe a reach\u2013align\u2013slide mechanism in reverse diffusion: samples enter a ridge neighborhood, approach the ridge in normal directions, and move along it relative to nearby training data. Our analysis relates alignment and local tangential motion to directional components of the learned denoising error, connecting training error to generation geometry. This perspective helps explain how generated samples can organize around structures induced by the data while differing from individual training examples. Synthetic examples and MNIST latent-space experiments illustrate the predicted behavior. The talk will introduce the necessary background on diffusion models and log-density ridges.\n\nThis talk is based on joint work with Yitong Qiu and Molei Tao, recently accepted at NeurIPS 2026.\n\nContact: Zhiyan Ding", "occurrence_notes":null, "guid":"148881-21905043@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/148881", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"1084", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics","Applied Mathematics"], "website":"", "sponsors":[ { "group_name":"Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics", "group_id":"4882", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21905043 } , "148882-21905044": { "datetime_modified":"20261020T211151", "datetime_start":"20261113T150000", "datetime_end":"20261113T160000", "has_end_time":1, "date_start":"2026-11-13", "date_end":"2026-11-13", "time_start":"15:00:00", "time_end":"16:00:00", "time_zone":"America\/Detroit", "event_title":"AIM Seminar: Geometry for Physics Simulation", "occurrence_title":"", "combined_title":"AIM Seminar: Geometry for Physics Simulation: Oliver Gross (Computer Science and Engineering, University of California San Diego)", "event_subtitle":"Oliver Gross (Computer Science and Engineering, University of California San Diego)", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"Abstract: Advances in simulation and scientific machine learning have made computation an engine of discovery. For increasingly complex physical systems, however, computational scale and model expressiveness alone may not suffice for faithful simulation, exploration, and inverse design. General-purpose representations often describe a space much larger than the set of physically admissible states. Computing in this larger space can require substantial effort to ensure that solutions respect the underlying geometry, topology, and conservation laws. A complementary path is to make this structure explicit. Through examples ranging from bending rods and slithering snakes to fluid flows and magnetic fields in plasmas, this talk shows how geometric insight can make difficult problems computationally tractable, how the resulting structure can be preserved and encoded in algorithms, and how the exchange among theory, discretization, and application yields new mathematics alongside more effective computational tools.\n\n\nContact: Ian Tobasco", "occurrence_notes":null, "guid":"148882-21905044@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/148882", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"1084", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Applied Mathematics","Mathematics"], "website":"", "sponsors":[ { "group_name":"Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics", "group_id":"4882", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21905044 } , "148883-21905045": { "datetime_modified":"20260920T132120", "datetime_start":"20261120T150000", "datetime_end":"20261120T160000", "has_end_time":1, "date_start":"2026-11-20", "date_end":"2026-11-20", "time_start":"15:00:00", "time_end":"16:00:00", "time_zone":"America\/Detroit", "event_title":"AIM Seminar: Title TBA", "occurrence_title":"", "combined_title":"AIM Seminar: Title TBA: Hongrui Chen (Mathematics, Stanford)", "event_subtitle":"Hongrui Chen (Mathematics, Stanford)", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"Abstract: TBA\n\nContact: Zhiyan Ding", "occurrence_notes":null, "guid":"148883-21905045@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/148883", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"1084", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Applied Mathematics","Mathematics"], "website":"", "sponsors":[ { "group_name":"Applied Interdisciplinary Mathematics (AIM) Seminar - 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