Sergio Rozada
Publications
DiPhon: Diffusion on Graphons for Scalable Graph Generation
Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem. We approach this question in the dense-graph setting through the lens of graphons, the size-agnostic limit objects of dense graph sequences, to study how structural graph statistics behave across node-size scales. This perspective leads to DiPhon, a diffusion framework for size-scalable graph generation. Specifically, we formulate a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), and propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs. We further derive the corresponding reverse-time process, which requires access to the marginal score. For the Jacobi process, this score interestingly admits a tractable form, which we estimate from data via graph denoising and plug into the reverse process to generate graph samples. We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy. Thus, DiPhon inherits key size-agnostic statistical properties of the graphon dynamics, providing a principled route toward scalable graph generation. Empirically, we demonstrate this scalability by training on small graphs and generating progressively larger graphs at inference time, without retraining, while preserving their core topological properties.
Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att
Learning Policy Representations for Steerable Behavior Synthesis
Given a Markov decision process (MDP), we seek to learn representations for a range of policies to facilitate behavior steering at test time. As policies of an MDP are uniquely determined by their occupancy measures, we propose modeling policy representations as expectations of state-action feature maps with respect to occupancy measures. We show that these representations can be approximated uniformly for a range of policies using a set-based architecture. Our model encodes a set of state-action samples into a latent embedding, from which we decode both the policy and its value functions corresponding to multiple rewards. We use variational generative approach to induce a smooth latent space, and further shape it with contrastive learning so that latent distances align with differences in value functions. This geometry permits gradient-based optimization directly in the latent space. Leveraging this capability, we solve a novel behavior synthesis task, where policies are steered to satisfy previously unseen value function constraints without additional training.