arXiv subjects

Nicolas Zilberstein

Publications and source records attributed to Nicolas Zilberstein.

16 recordsLinked to original sources

arXiv2026

Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems

Image restoration faces a fundamental tradeoff: methods that minimize error produce blurry reconstructions, while those that maximize perceptual quality yield sharp but less faithful images. Existing approaches either commit to a single operating point on this distortion perception (DP) frontier or require paired-data supervision, auxiliary models, or hyperparameter tuning of the sampler to access different points. We show that flow map models, a recent extension of flow matching for few-step sampling that learns an average field, implicitly define a one-parameter family of denoisers that continuously spans the DP frontier. The lookahead parameter t acts as a control knob between the MMSE and perceptual regimes. For Gaussian targets, we prove that varying t exactly recovers the optimal DP frontier; for natural images, we observe similar behavior empirically. Within a Plug-and-Play solver, the same mechanism extends to general inverse problems, where it controls a tradeoff between perceptual alignment and data consistency. Despite the lack of exact optimality guarantees in this setting, a single trained flow map spans the DP tradeoff, matching or exceeding specialized baselines at both extremes. Extensive experiments on CelebA ($128\times 128$) and AFHQ ($256\times 256$) across several linear and nonlinear inverse tasks validate our findings.

cs.LG↗

arXiv2026

Learning Normalized Energy Models for Linear Inverse Problems

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

cs.LG↗

arXiv2026

Prior-Informed Flow Matching for Graph Reconstruction

We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while modern generative models struggle to incorporate structural priors. PIFM bridges this gap by integrating embedding-based priors with continuous-time flow matching. Grounded in a permutation equivariant version of the distortion-perception theory, our method first uses a prior, such as GraphSAGE or node2vec, to form an informed initial estimate of the adjacency matrix based on local information. It then applies rectified flow matching to refine this estimate, transporting it toward the true distribution of clean graphs and learning a global coupling. Experiments on different datasets demonstrate that PIFM consistently enhances classical embeddings, outperforming them and state-of-the-art generative baselines in reconstruction accuracy.

cs.LG↗

arXiv2025

Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials

We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.

stat.CO↗

arXiv2025

Model-Driven Graph Contrastive Learning

We propose $\textbf{MGCL}$, a model-driven graph contrastive learning (GCL) framework that leverages graphons (probabilistic generative models for graphs) to guide contrastive learning by accounting for the data's underlying generative process. GCL has emerged as a powerful self-supervised framework for learning expressive node or graph representations without relying on annotated labels, which are often scarce in real-world data. By contrasting augmented views of graph data, GCL has demonstrated strong performance across various downstream tasks, such as node and graph classification. However, existing methods typically rely on manually designed or heuristic augmentation strategies that are not tailored to the underlying data distribution and operate at the individual graph level, ignoring similarities among graphs generated from the same model. Conversely, in our proposed approach, MGCL first estimates the graphon associated with the observed data and then defines a graphon-informed augmentation process, enabling data-adaptive and principled augmentations. Additionally, for graph-level tasks, MGCL clusters the dataset and estimates a graphon per group, enabling contrastive pairs to reflect shared semantics and structure. Extensive experiments on benchmark datasets demonstrate that MGCL achieves state-of-the-art performance, highlighting the advantages of incorporating generative models into GCL.

cs.LG↗

arXiv2025

Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation

Diffusion models have emerged as powerful generative models for graph generation, yet their use for conditional graph generation remains a fundamental challenge. In particular, guiding diffusion models on graphs under arbitrary reward signals is difficult: gradient-based methods, while powerful, are often unsuitable due to the discrete and combinatorial nature of graphs, and non-differentiable rewards further complicate gradient-based guidance. We propose Graph Guided Diffusion (GGDiff), a novel guidance framework that interprets conditional diffusion on graphs as a stochastic control problem to address this challenge. GGDiff unifies multiple guidance strategies, including gradient-based guidance (for differentiable rewards), control-based guidance (using control signals from forward reward evaluations), and zero-order approximations (bridging gradient-based and gradient-free optimization). This comprehensive, plug-and-play framework enables zero-shot guidance of pre-trained diffusion models under both differentiable and non-differentiable reward functions, adapting well-established guidance techniques to graph generation--a direction largely unexplored. Our formulation balances computational efficiency, reward alignment, and sample quality, enabling practical conditional generation across diverse reward types. We demonstrate the efficacy of GGDiff in various tasks, including constraints on graph motifs, fairness, and link prediction, achieving superior alignment with target rewards while maintaining diversity and fidelity.

cs.LG↗

arXiv2024

Scalable Implicit Graphon Learning

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.

stat.ML↗

arXiv2024

Repulsive Latent Score Distillation for Solving Inverse Problems

Score Distillation Sampling (SDS) has been pivotal for leveraging pre-trained diffusion models in downstream tasks such as inverse problems, but it faces two major challenges: $(i)$ mode collapse and $(ii)$ latent space inversion, which become more pronounced in high-dimensional data. To address mode collapse, we introduce a novel variational framework for posterior sampling. Utilizing the Wasserstein gradient flow interpretation of SDS, we propose a multimodal variational approximation with a repulsion mechanism that promotes diversity among particles by penalizing pairwise kernel-based similarity. This repulsion acts as a simple regularizer, encouraging a more diverse set of solutions. To mitigate latent space ambiguity, we extend this framework with an augmented variational distribution that disentangles the latent and data. This repulsive augmented formulation balances computational efficiency, quality, and diversity. Extensive experiments on linear and nonlinear inverse tasks with high-resolution images ($512 \times 512$) using pre-trained Stable Diffusion models demonstrate the effectiveness of our approach.

cs.LG↗

arXiv2023

Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of our unknown variables of interest while being computationally more efficient than their first-order counterpart and the non-conditioned versions of both dynamics. Moreover, we prove that both pre-conditioned dynamics are well-defined and have the same unique invariant distributions as the non-conditioned cases. We also incorporate an annealing procedure that has the double benefit of further accelerating the convergence of the algorithm and allowing us to accommodate the case where the unknown variables are discrete. Numerical experiments in two different tasks in communications (MIMO symbol detection and channel estimation) and in three tasks for images showcase the generality of our method and illustrate the high performance achieved relative to competing approaches (including learning-based ones) while having comparable or lower computational complexity.

stat.ML↗

arXiv2023

Joint channel estimation and data detection in massive MIMO systems based on diffusion models

We propose a joint channel estimation and data detection algorithm for massive multilple-input multiple-output systems based on diffusion models. Our proposed method solves the blind inverse problem by sampling from the joint posterior distribution of the symbols and channels and computing an approximate maximum a posteriori estimation. To achieve this, we construct a diffusion process that models the joint distribution of the channels and symbols given noisy observations, and then run the reverse process to generate the samples. A unique contribution of the algorithm is to include the discrete prior distribution of the symbols and a learned prior for the channels. Indeed, this is key as it allows a more efficient exploration of the joint search space and, therefore, enhances the sampling process. Through numerical experiments, we demonstrate that our method yields a lower normalized mean squared error than competing approaches and reduces the pilot overhead.

eess.SP↗

arXiv2023

Annealed Langevin Dynamics for Massive MIMO Detection

Solving the optimal symbol detection problem in multiple-input multiple-output (MIMO) systems is known to be NP-hard. Hence, the objective of any detector of practical relevance is to get reasonably close to the optimal solution while keeping the computational complexity in check. In this work, we propose a MIMO detector based on an annealed version of Langevin (stochastic) dynamics. More precisely, we define a stochastic dynamical process whose stationary distribution coincides with the posterior distribution of the symbols given our observations. In essence, this allows us to approximate the maximum a posteriori estimator of the transmitted symbols by sampling from the proposed Langevin dynamic. Furthermore, we carefully craft this stochastic dynamic by gradually adding a sequence of noise with decreasing variance to the trajectories, which ensures that the estimated symbols belong to a pre-specified discrete constellation. Based on the proposed MIMO detector, we also design a robust version of the method by unfolding and parameterizing one term -- the score of the likelihood -- by a neural network. Through numerical experiments in both synthetic and real-world data, we show that our proposed detector yields state-of-the-art symbol error rate performance and the robust version becomes noise-variance agnostic.

eess.SP↗

arXiv2023

Unsupervised Learning of Sampling Distributions for Particle Filters

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.

eess.SP↗

arXiv2022

Accelerated massive MIMO detector based on annealed underdamped Langevin dynamics

We propose a multiple-input multiple-output (MIMO) detector based on an annealed version of the \emph{underdamped} Langevin (stochastic) dynamic. Our detector achieves state-of-the-art performance in terms of symbol error rate (SER) while keeping the computational complexity in check. Indeed, our method can be easily tuned to strike the right balance between computational complexity and performance as required by the application at hand. This balance is achieved by tuning hyperparameters that control the length of the simulated Langevin dynamic. Through numerical experiments, we demonstrate that our detector yields lower SER than competing approaches (including learning-based ones) with a lower running time compared to a previously proposed \emph{overdamped} Langevin-based MIMO detector.

eess.SP↗

arXiv2022

Detection by Sampling: Massive MIMO Detector based on Langevin Dynamics

Optimal symbol detection in multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Hence, the objective of any detector of practical relevance is to get reasonably close to the optimal solution while keeping the computational complexity in check. In this work, we propose a MIMO detector based on an annealed version of Langevin (stochastic) dynamics. More precisely, we define a stochastic dynamical process whose stationary distribution coincides with the posterior distribution of the symbols given our observations. In essence, this allows us to approximate the maximum a posteriori estimator of the transmitted symbols by sampling from the proposed Langevin dynamic. Furthermore, we carefully craft this stochastic dynamic by gradually adding a sequence of noise with decreasing variance to the trajectories, which ensures that the estimated symbols belong to a pre-specified discrete constellation. Through numerical experiments, we show that our proposed detector yields state-of-the-art symbol error rate performance.

eess.SP↗

arXiv2021

Robust MIMO Detection using Hypernetworks with Learned Regularizers

Optimal symbol detection in multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Recently, there has been a growing interest to get reasonably close to the optimal solution using neural networks while keeping the computational complexity in check. However, existing work based on deep learning shows that it is difficult to design a generic network that works well for a variety of channels. In this work, we propose a method that tries to strike a balance between symbol error rate (SER) performance and generality of channels. Our method is based on hypernetworks that generate the parameters of a neural network-based detector that works well on a specific channel. We propose a general framework by regularizing the training of the hypernetwork with some pre-trained instances of the channel-specific method. Through numerical experiments, we show that our proposed method yields high performance for a set of prespecified channel realizations while generalizing well to all channels drawn from a specific distribution.

eess.SP↗

arXiv2021

Unrolling Particles: Unsupervised Learning of Sampling Distributions

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate samples where only one trajectory carries all the weight, negatively affecting the resulting performance of the estimate. While much research has been done on the design of appropriate sampling distributions that would lead to controlled degeneracy, in this paper our objective is to \emph{learn} sampling distributions. Leveraging the framework of algorithm unrolling, we model the sampling distribution as a multivariate normal, and we use neural networks to learn both the mean and the covariance. We carry out unsupervised training of the model to minimize weight degeneracy, relying only on the observed measurements of the system. We show in simulations that the resulting particle filter yields good estimates in a wide range of scenarios.

cs.LG↗