A conditional generative model is a method for sampling from a conditional distribution $p(y \mid x)$. For example, one may want to sample an image of a cat given the label ``cat''. A feed-forward conditional generative model is a function $g(x, z)$ that takes the input $x$ and a random seed $z$, and outputs a sample $y$ from $p(y \mid x)$. Ideally the distribution of outputs $(x, g(x, z))$ would be close in total variation to the ideal distribution $(x, y)$.Generalization bounds for other learning models require assumptions on the distribution of $x$, even in simple settings like linear regression with Gaussian noise. We show these assumptions are unnecessary in our model, for both linear regression and single-layer ReLU networks. Given samples $(x, y)$, we show how to learn a 1-layer ReLU conditional generative model in total variation. As our result has no assumption on the distribution of inputs $x$, if we are given access to the internal activations of a deep generative model, we can compose our 1-layer guarantee to progressively learn the deep model using a near-linear number of samples.

Deep generative models (DGMs) of images are now sufficiently mature that they produce nearly photorealistic samples and obtain scores similar to the data distribution on heuristics such as Frechet Inception Distance (FID). These results, especially on large-scale datasets such as ImageNet, suggest that DGMs are learning the data distribution in a perceptually meaningful space and can be used in downstream tasks. To test this latter hypothesis, we use class-conditional generative models from a number of model classes--variational autoencoders, autoregressive models, and generative adversarial networks (GANs)--to infer the class labels of real data. We perform this inference by training an image classifier using only synthetic data and using the classifier to predict labels on real data. The performance on this task, which we call Classification Accuracy Score (CAS), reveals some surprising results not identified by traditional metrics and constitute our contributions. First, when using a state-of-the-art GAN (BigGAN-deep), Top-1 and Top-5 accuracy decrease by 27.9% and 41.6%, respectively, compared to the original data; and conditional generative models from other model classes, such as Vector-Quantized Variational Autoencoder-2 (VQ-VAE-2) and Hierarchical Autoregressive Models (HAMs), substantially outperform GANs on this benchmark. Second, CAS automatically surfaces particular classes for which generative models failed to capture the data distribution, and were previously unknown in the literature. Third, we find traditional GAN metrics such as Inception Score (IS) and FID neither predictive of CAS nor useful when evaluating non-GAN models. Furthermore, in order to facilitate better diagnoses of generative models, we open-source the proposed metric.

Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy desired constraints or exhibit desired properties is difficult. In practice, expensive heuristic search or reinforcement learning algorithms are often employed. In this paper, we investigate the use of conditional generative models which directly attack this inverse problem, by modeling the distribution of discrete structures given properties of interest. Unfortunately, the maximum likelihood training of such models often fails with the samples from the generative model inadequately respecting the input properties. To address this, we introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We avoid high-variance score-function estimators that would otherwise be required by sampling from an approximation to the normalized rewards, allowing simple Monte Carlo estimation of model gradients. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value. In both cases, we find improvements over maximum likelihood estimation and other baselines.

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

Figure 1: A conditional distribution defined by a conditional generative model.

Training datasets are inherently imperfect, often containing mislabeled samples due to human annotation errors, limitations of tagging models, and other sources of noise. Such label contamination can significantly degrade the performance of a trained model. In this work, we introduce Self-Purifying Flow Matching (SPFM), a principled approach to filtering unreliable data within the flow-matching framework. SPFM identifies suspicious data using the model itself during the training process, bypassing the need for pretrained models or additional modules. Our experiments demonstrate that models trained with SPFM generate samples that accurately adhere to the specified conditioning, even when trained on noisy labels. Furthermore, we validate the robustness of SPFM on the TITW dataset, which consists of in-the-wild speech data, achieving performance that surpasses existing baselines.

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