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1. Generative Marginalization Models

   Liu, Sulin; Ramadge, Peter; Adams, Ryan P (July 2024, MLR)

   We introduce marginalization models (MAMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling by explicitly modeling all induced marginal distributions. Marginalization models enable fast approximation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of arbitrary marginal inference models, such as any-order autoregressive models. MAMs also address the scalability bottleneck encountered in training any-order generative models for high-dimensional problems under the context of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized log-probability function such as energy or reward function). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including images, text, physical systems, and molecules, for maximum likelihood and energy-based training settings. MAMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MAMs enable any-order generative modeling of high-dimensional problems beyond the scale of previous methods. 

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2. Multisample Flow Matching: Straightening Flows with Minibatch Couplings

   Pooladian, Aram-Alexandre; Ben-Hamu, Heli; Domingo-Enrich, Carles; Amos, Brandon; Lipman, Yaron; Chen, Ricky T. (May 2023, ICML 2023)

   Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation. 

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3. SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics

   https://doi.org/10.1016/j.jcp.2024.113442  

   Stinis, P; Daskalakis, C; Atzberger, PJ (December 2024, Journal of Computational Physics)

   We introduce adversarial learning methods for data-driven generative modeling of dynamics of n-th-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems. 

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4. Accelerating NCE Convergence with Adaptive Normalizing Constant Computation

   Chikina, Maria; Koes, David; Sevekari, Anish; Aggarwal, Rishal (July 2024, Open Review)

   Noise Contrastive Estimation (NCE) is a widely used method for training generative models, typically used as an alternative to Maximum Likelihood Estimation (MLE) when exact computations of probability are hard. NCE trains generative models by discriminating between data and appropriately chosen noise distributions. Although NCE is statistically consistent, it suffers from slow convergence and high variance when there is small overlap between the noise and data distributions. Both these problems are related to the flatness of the NCE loss landscape. We propose an innovative approach to circumvent slow convergence rates by quick inference of the optimal normalizing constant at every gradient step. This allows the rest of the parameters to have more freedom during NCE optimization. We analyze the use of both binary search and the Bennett Acceptance Ratio (BAR) for quick computation of the normalizing constant and show improved performance for both methods on convex and non-convex settings. 

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5. Learning energy-based models by diffusion recovery likelihood

   Gao, R.; Song, Y.; Poole, B.; Wu, Y. N.; Kingma, D. P. (April 2021, International Conference on Learning Representations (ICLR 2021))

   While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion re- covery likelihood method to tractably learn and sample from a sequence of EBMs trained on increasingly noisy versions of a dataset. Each EBM is trained with recovery likelihood, which maximizes the conditional probability of the data at a certain noise level given their noisy versions at a higher noise level. Optimizing re- covery likelihood is more tractable than marginal likelihood, as sampling from the conditional distributions is much easier than sampling from the marginal distribu- tions. After training, synthesized images can be generated by the sampling process that initializes from Gaussian white noise distribution and progressively samples the conditional distributions at decreasingly lower noise levels. Our method gener- ates high fidelity samples on various image datasets. On unconditional CIFAR-10 our method achieves FID 9.58 and inception score 8.30, superior to the majority of GANs. Moreover, we demonstrate that unlike previous work on EBMs, our long-run MCMC samples from the conditional distributions do not diverge and still represent realistic images, allowing us to accurately estimate the normalized density of data even for high-dimensional datasets. Our implementation is avail- able at https://github.com/ruiqigao/recovery_likelihood. 

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