Statistical Foundations of Generative Modeling

TBA

This talk presents a sequence of recent results on Joint-Embedding Predictive Architectures (JEPAs), spanning self-supervised representation learning, action-conditioned world models, and counterfactual reasoning. We begin with LeJEPA, which addresses representation collapse through a distributional principle: embeddings are regularized toward an isotropic Gaussian using Sketched Isotropic Gaussian Regularization, producing a simple predictive objective with theoretical guarantees and without teacher–student networks or stop-gradient heuristics. We then introduce LeWorldModel, which extends this construction to sequential data by learning an encoder and action-conditioned latent transition model, (z_{t+1} approx f_theta(z_t,a_t)), end-to-end from raw observations. By combining next-embedding prediction with Gaussian latent regularization, the model supports planning and control directly in representation space, without reconstructing future pixels. Finally, we discuss new directions in counterfactual JEPAs, where object-level masking and latent interventions create structured partial-observability problems that force the predictor to model interaction-dependent dynamics rather than exploit local correlations. Throughout, we emphasize the geometric and statistical principles connecting these methods, and ask when latent prediction is sufficient for learning causal, controllable abstractions of a dynamical world.

Flow matching drives many of today's generative models. The standard recipe is simple: learn the average velocity that carries noise to data, then integrate it. But averaging discards structure. When a point could plausibly move toward several destinations, the mean velocity points somewhere between them, and the multimodal geometry of the transport is lost. This talk asks what happens if we keep that structure. Rather than regressing the conditional mean velocity, CCVFM models the full conditional law of the velocity 𝑉 =𝑋1 −𝑋0. What makes this tractable is a surrogate: replace the target by an entropy-regularized coreset, a Gaussian mixture with far fewer components than there are data points, and the induced conditional velocity law becomes available in closed form. A Sinkhorn-anchored coupling then pairs source and data velocities so that the surrogate marginal is preserved exactly and pairs concentrate on matched mixture components. The construction also closes a gap between theory and practice. Known rates for flow matching leave slack in the exponent, and the proofs rely on a diffusion-style path with the time interval partitioned into subintervals, each handled by a separately trained network. Deployed flow matching does none of this. We obtain the exact minimax exponent using a single global network on a linear path, with no time partition. Experiments on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ confirm the predicted regime.

Generative models are typically evaluated by the realism of their synthetic data. In biomedical research, however, the data themselves are rarely the ultimate object of interest. What matters is whether a generative model improves inference about effects of interest when data are scarce or difficult to collect, as in rare-disease trials, small patient subgroups, or rare cell states. This talk examines a fundamental limitation: any information a generative model contributes to an inference problem must come from its training data or from prior knowledge and assumptions encoded in the model, its architecture, or its training objective. Successful uses of generative models for inference include synthetic control arms in rare-disease trials and synthetic null distributions for false-discovery-rate control in differential-expression analysis. In these examples, synthetic data serve as flexible devices for encoding informative priors or statistical null hypotheses, respectively. When synthetic data are added to real data to improve power, the potential benefit follows a classical bias–variance trade-off: variance may decrease, but bias can increase when the encoded prior is misspecified. I relate this problem to prediction-powered inference, where a debiasing rectifier comparing predicted and observed labels is needed to obtain validity guarantees. Comparable guarantees are less straightforward for what one might call generation-powered inference. For example, single-cell foundation models trained on atlas data dominated by normal conditions face fundamental limitations in generating cells from previously unseen biological conditions and may underperform simple baselines. I contrast generation-powered inference with generation-calibrated inference, in which synthetic data are generated to reflect a null hypothesis under test. Whereas generation-powered inference requires scrutiny of the encoded prior and tools to quantify or control its induced bias, generation-calibrated inference is often more tractable: its goal is valid calibration under a specified null. Our work on scDesign3, ClusterDE, and Nullstrap illustrates this latter approach. I argue that, beyond realism, generative models should be judged by criteria appropriate to their inferential role, including calibration, coverage, bias–variance trade-offs, and robustness to discrepancies between the generative model and the true data-generating process.