Abstract Diffusion models consistently produce stunningly realistic signals, including images, videos and robotic trajectories, but they also frequently synthesize signals that hallucinate. Building a reliable pipeline free of structural hallucinations forces us to ask key questions: can we prove that diffusion models will never hallucinate? Should we rely on deterministic …
Abstract Averaging is one of the oldest ideas in signal processing. Average noisy measurements and the noise fades. Average over all plausible answers and you get the minimum mean squared error estimate. Today, the same principle sits at the heart of the diffusion and flow models behind modern generative AI. …
Abstract Nonconvex optimization is central to modern computational algorithms, with first-order methods playing a leading role because of their low cost per iteration. Although saddle points can obstruct progress toward local minima, gradient descent and certain momentum methods almost surely avoid converging to strict saddles under suitable assumptions. Prior work …
Abstract Transport-based models such as score-based diffusion and flow matching have become a leading paradigm for generative modeling: given samples from a distribution, one learns dynamics that produce new ones. Many scientific problems do not come in this form. The distribution of interest may be a tilted version of one …
Abstract Large language model (LLM) judges are increasingly used to monitor the outputs of LLM-based AI agents, yet formal guarantees on the reliability of these judges remain largely absent, limiting confidence in their use for safety-critical oversight. In this talk, I will consider certifying such judges and formalize their risk …
Abstract Newton and interior-point methods ask, at every iteration, for two derivative matrices: the Jacobian of the constraints and the Hessian of the Lagrangian. Automatic differentiation (AD) can produce both from nothing more than a program that evaluates the functions. But AD does not return a matrix. It returns an …
Abstract Flow and diffusion models define processes that generate samples from progressively less noisy versions of the data distribution. I will present a line of work on estimating the marginal probability densities along these processes, culminating in the density of the data distribution itself. Our methods are both sample-efficient to …
Abstract A central objective of modern generative AI is to enable learning and inference across multiple modalities, supporting tasks such as cross-modal generation, multimodal translation, domain transfer, and data fusion. Despite impressive empirical progress, many multimodal AI frameworks still lack solid theoretical foundations, raising concerns about reliability and robustness. In …
Abstract Assortment and inventory decisions lie at the core of supply chain and retail operations. In many settings, these decisions are complicated by customer substitution: when a preferred product is unavailable, customers may switch to other products, and as inventory is depleted over time, the demand faced by the remaining …