Searching for novel and diverse molecular candidates is a critical undertaking in drug and material discovery. Existing approaches have successfully adapted the diffusion model, the most effective generative model in image generation, to create 1D SMILES strings, 2D chemical graphs, or 3D molecular conformers. However, these methods are not efficient and flexible enough to generate 3D molecules with multiple desired properties, as they require additional training for the models for each new property or even a new combination of existing properties. Moreover, some properties may potentially conflict, making it impossible to find a molecule that satisfies all of them simultaneously. To address these challenges, we present a training-free conditional 3D molecular generation algorithm based on off-the-shelf unconditional diffusion models and property prediction models. The key techniques include modeling the loss of property prediction models as energy functions, considering the property relation between multiple conditions as a probabilistic graph, and developing a stable posterior estimation for computing the conditional score function. We conducted experiments on both single-objective and multi-objective 3D molecule generation, focusing on quantum properties, and compared our approach with the trained or fine-tuned diffusion models. Our proposed model achieves superior performance in generating molecules that meet the conditions, without any additional training cost.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations.

We consider the problem of fitting autoregressive graph generative models via maximum likelihood estimation (MLE). MLE is intractable for graph autoregressive models because the nodes in a graph can be arbitrarily reordered; thus the exact likelihood involves a sum over all possible node orders leading to the same graph. In this work, we fit the graph models by maximizing a variational bound, which is built by first deriving the joint probability over the graph and the node order of the autoregressive process. This approach avoids the need to specify ad-hoc node orders, since an inference network learns the most likely node sequences that have generated a given graph. We improve the approach by developing a graph generative model based on attention mechanisms and an inference network based on routing search. We demonstrate empirically that fitting autoregressive graph models via variational inference improves their qualitative and quantitative performance, and the improved model and inference network further boost the performance.

When formulated as an unsupervised learning problem, anomaly detection often requires a model to learn the distribution of normal data. Previous works modify Generative Adversarial Networks (GANs) by using encoder-decoders as generators and apply them to anomaly detection tasks. Previous studies indicate that GAN ensembles are often more stable than single GANs in image generation tasks. In this work, we propose to construct GAN ensembles for anomaly detection. In the proposed method, a group of generators interact with a group of discriminators, so every generator gets feedback from every discriminator, and vice versa. Compared to a single GAN, an ensemble of GANs can better model the distribution of normal data and thus better detect anomalies. We also make a theoretical analysis of GANs and GAN ensembles in the context of anomaly detection. The empirical study constructs ensembles based on four different types of detecting models, and the results show that the ensemble outperforms the single model for all four model types.

A graph generative model defines a distribution over graphs. Typically, the model consists of a sequential process that creates and adds nodes and edges. Such sequential process defines an ordering of the nodes in the graph. The computation of the model’s likelihood requires to marginalize the node orderings; this makes maximum likelihood estimation (MLE) challenging due to the (factorial) number of possible permutations. In this work, we provide an expression for the likelihood of a graph generative model and show that its calculation is closely related to the problem of graph automorphism. In addition, we derive a variational inference (VI) algorithm for fitting a graph generative model that is based on the maximization of a variational bound of the log-likelihood. This allows the model to be trained with node orderings from the approximate posterior instead of ad-hoc orderings. Our experiments show that our log-likelihood bound is significantly tighter than the bound of previous schemes. The models fitted with the VI algorithm are able to generate high-quality graphs that match the structures of target graphs not seen during training.