About

Stefano Ermon leads research that focuses on innovative computational approaches to address societal and environmental challenges of the 21st century. His work combines foundational research in artificial intelligence and machine learning with practical applications in science and engineering. The goal of his research is to enable computers to act intelligently and adaptively in increasingly complex and uncertain real-world environments.

Research topics

• Computer Science
• Artificial Intelligence
• Machine Learning
• Engineering
• Data science
• Algorithm
• Mathematics
• Remote sensing
• Geography
• Applied mathematics
• Theoretical computer science
• Political Science
• Mathematical optimization
• Genetics
• Engineering ethics
• Computational biology
• Management science
• Biology
• Ecology
• Computer vision
• Psychology
• Law
• Reliability engineering
• Parallel computing

Selected publications

• TFG-Flow: Training-free Guidance in Multimodal Generative Flow

  ArXiv.org · 2025-01-24

  preprintOpen access

  Given an unconditional generative model and a predictor for a target property (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. As a highly efficient technique for steering generative models toward flexible outcomes, training-free guidance has gained increasing attention in diffusion models. However, existing methods only handle data in continuous spaces, while many scientific applications involve both continuous and discrete data (referred to as multimodality). Another emerging trend is the growing use of the simple and general flow matching framework in building generative foundation models, where guided generation remains under-explored. To address this, we introduce TFG-Flow, a novel training-free guidance method for multimodal generative flow. TFG-Flow addresses the curse-of-dimensionality while maintaining the property of unbiased sampling in guiding discrete variables. We validate TFG-Flow on four molecular design tasks and show that TFG-Flow has great potential in drug design by generating molecules with desired properties.

  PublisherOA PDFDOI

• Probabilistic Graphical Models: A Concise Tutorial

  ArXiv.org · 2025-07-23

  preprintOpen access

  Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tutorial provides a concise introduction to the formalisms, methods, and applications of this modeling framework. After a review of basic probability and graph theory, we explore three dominant themes: (1) the representation of multivariate distributions in the intuitive visual language of graphs, (2) algorithms for learning model parameters and graphical structures from data, and (3) algorithms for inference, both exact and approximate.

  PublisherOA PDFDOI

• RFG: Test-Time Scaling for Diffusion Large Language Model Reasoning with Reward-Free Guidance

  ArXiv.org · 2025-09-29

  preprintOpen accessSenior author

  Diffusion large language models (dLLMs) have shown great potential in large-scale language modeling, and there is an increasing interest in further improving the capacity to solve complex problems by guiding the reasoning process step by step. Common practice for autoregressive language models typically learns a process reward model with dense annotation for each intermediate step. However, this is challenging for dLLMs where the generation is in an any-order fashion and intermediate states are partially masked sentences. To this end, in this paper, we propose reward-free guidance (RFG), a principled method for guiding the reasoning trajectory of dLLMs without explicit process reward. The key idea of RFG is to parameterize the process reward by log-likelihood ratios of the enhanced and reference dLLMs, where the enhanced model can be easily obtained by any off-the-shelf dLLM that has been post-trained with reinforcement learning (RL) or supervised fine-tuning (SFT). We provide theoretical justification that RFG induces the reward-guided sampling distribution with no additional reward. We conduct comprehensive experiments on four challenging mathematical reasoning and code generation benchmarks using a diverse suite of dLLMs enhanced with various post-training methods. RFG consistently yields significant improvements across all tasks and model types, achieving accuracy gains of up to 9.2%. These findings establish RFG as a general training-free framework that scales test-time reasoning without reliance on external reward models.

  PublisherOA PDFDOI

• Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints

  ArXiv.org · 2025-07-06

  preprintOpen access

  Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38% to 84% on different cyclization strategies.

  PublisherOA PDFDOI

• Aligning Large Language Models with Human Feedback: Mathematical Foundations and Algorithm Design

  2025-05-21

  preprintOpen access

  This article provides an introduction to the mathematical foundations and algorithmic frameworks used to align Large Language Models (LLMs) with human intentions, preferences, and values. We discuss standard alignment techniques, such as fine-tuning (SFT), reinforcement learning with human feedback (RLHF), and direct preference optimization (DPO). We also explore the theoretical underpinnings of learning from human preferences, drawing connections to inverse reinforcement learning (IRL) and discrete choice models. We present state-of-the-art algorithms in a tutorial style, discuss their advantages and limitations, and offer insights into practical implementation. Our exposition is intended to serve as a comprehensive resource for researchers and practitioners, providing both a foundational understanding of alignment methodologies and a framework for developing more robust and scalable alignment techniques.

  PublisherOA PDFDOI

• Inductive Moment Matching

  ArXiv.org · 2025-03-10

  preprintOpen access

  Diffusion models and Flow Matching generate high-quality samples but are slow at inference, and distilling them into few-step models often leads to instability and extensive tuning. To resolve these trade-offs, we propose Inductive Moment Matching (IMM), a new class of generative models for one- or few-step sampling with a single-stage training procedure. Unlike distillation, IMM does not require pre-training initialization and optimization of two networks; and unlike Consistency Models, IMM guarantees distribution-level convergence and remains stable under various hyperparameters and standard model architectures. IMM surpasses diffusion models on ImageNet-256x256 with 1.99 FID using only 8 inference steps and achieves state-of-the-art 2-step FID of 1.98 on CIFAR-10 for a model trained from scratch.

  PublisherOA PDFDOI

• Training-Free Safe Denoisers for Safe Use of Diffusion Models

  ArXiv.org · 2025-02-11

  preprintOpen access

  There is growing concern over the safety of powerful diffusion models (DMs), as they are often misused to produce inappropriate, not-safe-for-work (NSFW) content or generate copyrighted material or data of individuals who wish to be forgotten. Many existing methods tackle these issues by heavily relying on text-based negative prompts or extensively retraining DMs to eliminate certain features or samples. In this paper, we take a radically different approach, directly modifying the sampling trajectory by leveraging a negation set (e.g., unsafe images, copyrighted data, or datapoints needed to be excluded) to avoid specific regions of data distribution, without needing to retrain or fine-tune DMs. We formally derive the relationship between the expected denoised samples that are safe and those that are not safe, leading to our $\textit{safe}$ denoiser which ensures its final samples are away from the area to be negated. Inspired by the derivation, we develop a practical algorithm that successfully produces high-quality samples while avoiding negation areas of the data distribution in text-conditional, class-conditional, and unconditional image generation scenarios. These results hint at the great potential of our training-free safe denoiser for using DMs more safely.

  PublisherOA PDFDOI

• Systems and Algorithms for Convolutional Multi-Hybrid Language Models at Scale

  ArXiv.org · 2025-02-25 · 3 citations

  articleOpen access

  We introduce convolutional multi-hybrid architectures, with a design grounded on two simple observations. First, operators in hybrid models can be tailored to token manipulation tasks such as in-context recall, multi-token recall, and compression, with input-dependent convolutions and attention offering complementary performance. Second, co-designing convolution operators and hardware-aware algorithms enables efficiency gains in regimes where previous alternative architectures struggle to surpass Transformers. At the 40 billion parameter scale, we train end-to-end 1.2 to 2.9 times faster than optimized Transformers, and 1.1 to 1.4 times faster than previous generation hybrids. On H100 GPUs and model width 4096, individual operators in the proposed multi-hybrid StripedHyena 2 architecture achieve two-fold throughput improvement over linear attention and state-space models. Multi-hybrids excel at sequence modeling over byte-tokenized data, as demonstrated by the Evo 2 line of models. We discuss the foundations that enable these results, including architecture design, overlap-add blocked kernels for tensor cores, and dedicated all-to-all and point-to-point context parallelism strategies.

  PublisherOA PDF

• RelDiff: Relational Data Generative Modeling with Graph-Based Diffusion Models

  ArXiv.org · 2025-05-31

  preprintOpen access

  Real-world databases are predominantly relational, comprising multiple interlinked tables that contain complex structural and statistical dependencies. Learning generative models on relational data has shown great promise in generating synthetic data and imputing missing values. However, existing methods often struggle to capture this complexity, typically reducing relational data to conditionally generated flat tables and imposing limiting structural assumptions. To address these limitations, we introduce RelDiff, a novel diffusion generative model that synthesizes complete relational databases by explicitly modeling their foreign key graph structure. RelDiff combines a joint graph-conditioned diffusion process across all tables for attribute synthesis, and a $2K+$SBM graph generator based on the Stochastic Block Model for structure generation. The decomposition of graph structure and relational attributes ensures both high fidelity and referential integrity, both of which are crucial aspects of synthetic relational database generation. Experiments on 11 benchmark datasets demonstrate that RelDiff consistently outperforms prior methods in producing realistic and coherent synthetic relational databases. Code is available at https://github.com/ValterH/RelDiff.

  PublisherOA PDFDOI

• InfoTok: Adaptive Discrete Video Tokenizer via Information-Theoretic Compression

  Open MIND · 2025-12-18

  preprint

  Accurate and efficient discrete video tokenization is essential for long video sequences processing. Yet, the inherent complexity and variable information density of videos present a significant bottleneck for current tokenizers, which rigidly compress all content at a fixed rate, leading to redundancy or information loss. Drawing inspiration from Shannon's information theory, this paper introduces InfoTok, a principled framework for adaptive video tokenization. We rigorously prove that existing data-agnostic training methods are suboptimal in representation length, and present a novel evidence lower bound (ELBO)-based algorithm that approaches theoretical optimality. Leveraging this framework, we develop a transformer-based adaptive compressor that enables adaptive tokenization. Empirical results demonstrate state-of-the-art compression performance, saving 20% tokens without influence on performance, and achieving 2.3x compression rates while still outperforming prior heuristic adaptive approaches. By allocating tokens according to informational richness, InfoTok enables a more compressed yet accurate tokenization for video representation, offering valuable insights for future research.

  DOI

Recent grants

• CAREER: Modeling and Inference for Large Scale Spatio-Temporal Data

  NSF · $540k · 2017–2024

• AitF: Collaborative Research: Efficient High-Dimensional Integration using Error-Correcting Codes

  NSF · $360k · 2017–2021

Frequent coauthors

• David B. Lobell

  82 shared

• Marshall Burke

  Stanford University

  71 shared

• Jiaming Song

  Hengshui University

  69 shared

• Alexandre Drouin

  63 shared

• Gabriel Huang

  63 shared

• Chenlin Meng

  Stanford University

  60 shared

• Burak Uzkent

  Amazon (United States)

  44 shared

• Aditya Grover

  41 shared

Awards & honors

• ICML 2024 Best Paper Award
• ICLR 2022 Outstanding Paper Award
• ICLR 2021 Outstanding Paper Award
• ISSNAF Young Investigator Award
• Sloan Research Fellowship