ICLR 2025 Papers

Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects with probabilities proportional to a given reward function. The key concept behind GFlowNets is the use of two stochastic policies: a forward policy, which incrementally constructs compositional objects, and a backward policy, which sequentially deconstructs them. Recent results show a close relationship between GFlowNet training and entropy-regularized reinforcement learning (RL) problems with a particular reward design. However, this connection applies only in the setting of a fixed backward policy, which might be a significant limitation. As a remedy to this problem, we introduce a simple backward policy optimization algorithm that involves direct maximization of the value function in an entropy-regularized Markov Decision Process (MDP) over intermediate rewards. We provide an extensive experimental evaluation of the proposed approach across various benchmarks in combination with both RL and GFlowNet algorithms and demonstrate its faster convergence and mode discovery in complex environments.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines. We also provide links to [project page](https://kiyoung98.github.io/tps-dps/) and [code](https://github.com/kiyoung98/tps-dps).

We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are absolutely continuous in the Wasserstein geometry. Second, we address specific interpolations $f_t$ and the learning of the related density/velocity pairs $(\rho_t,v_t)$. It was numerically observed that the linear interpolation, which requires only a parametrization of the velocity field $v_t$, suffers from a "teleportation-of-mass" issue. Using tools from the Wasserstein geometry, we give an analytical example, where we can precisely measure the explosion of the velocity field. Inspired by Máté and Fleuret, who parametrize both $f_t$ and $v_t$, we propose an interpolation which parametrizes only $f_t$ and fixes an appropriate $v_t$. This corresponds to the Wasserstein gradient flow of the Kullback-Leibler divergence related to Langevin dynamics. We demonstrate by numerical examples that our model provides a well-behaved flow field which successfully solves the above sampling task.

Speculative sampling is a promising approach to accelerate the decoding stage for Large Language Models (LLMs). Recent advancements that leverage target LLM's contextual information, such as hidden states and KV cache, have shown significant practical improvements. However, these approaches suffer from inconsistent context between training and decoding. We also observe another discrepancy between the training and decoding objectives in existing speculative sampling methods. In this work, we propose a solution named HArmonized Speculative Sampling (HASS) that learns harmonized representations to address these issues. HASS accelerates the decoding stage without adding inference overhead through harmonized objective distillation and harmonized context alignment. Experiments on four LLaMA models demonstrate that HASS achieves 2.81x-4.05x wall-clock time speedup ratio averaging across three datasets, surpassing EAGLE-2 by 8%-20%. The code is available at https://github.com/HArmonizedSS/HASS.

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.

Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo methods are the predominant tools for this task; however, both are often challenging to apply reliably, particularly when the posterior has complex geometry. Here, we introduce Soft Contrastive Variational Inference (SoftCVI), which allows a family of variational objectives to be derived through a contrastive estimation framework. The approach parameterizes a classifier in terms of a variational distribution, reframing the inference task as a contrastive estimation problem aiming to identify a single true posterior sample among a set of samples. Despite this framing, we do not require positive or negative samples, but rather learn by sampling the variational distribution and computing ground truth soft classification labels from the unnormalized posterior itself. The objectives have zero variance gradient when the variational approximation is exact, without the need for specialized gradient estimators. We empirically investigate the performance on a variety of Bayesian inference tasks, using both simple (e.g. normal) and expressive (normalizing flow) variational distributions. We find that SoftCVI can be used to form objectives which are stable to train and mass-covering, frequently outperforming inference with other variational approaches.

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been widely used. However, quantitative theoretical guarantees of these techniques are under-explored. This study takes a first step toward providing a non-asymptotic analysis of annealed MCMC. Specifically, we establish, for the first time, an oracle complexity of $\widetilde{O}\left(\frac{d\beta^2{\cal A}^2}{\varepsilon^6}\right)$ for the simple annealed Langevin Monte Carlo algorithm to achieve $\varepsilon^2$ accuracy in Kullback-Leibler divergence to the target distribution $\pi\propto{\rm e}^{-V}$ on $\mathbb{R}^d$ with $\beta$-smooth potential $V$. Here, ${\cal A}$ represents the action of a curve of probability measures interpolating the target distribution $\pi$ and a readily sampleable distribution.

This paper is motivated by recent research in the $d$-dimensional stochastic linear bandit literature, which has revealed an unsettling discrepancy: algorithms like Thompson sampling and Greedy demonstrate promising empirical performance, yet this contrasts with their pessimistic theoretical regret bounds. The challenge arises from the fact that while these algorithms may perform poorly in certain problem instances, they generally excel in typical instances. To address this, we propose a new data-driven technique that tracks the geometric properties of the uncertainty ellipsoid around the main problem parameter. This methodology enables us to formulate a data-driven frequentist regret bound, which incorporates the geometric information, for a broad class of base algorithms, including Greedy, OFUL, and Thompson sampling. This result allows us to identify and ``course-correct" problem instances in which the base algorithms perform poorly. The course-corrected algorithms achieve the minimax optimal regret of order $\tilde{\mathcal{O}}(d\sqrt{T})$ for a $T$-period decision-making scenario, effectively maintaining the desirable attributes of the base algorithms, including their empirical efficacy. We present simulation results to validate our findings using synthetic and real data.

Algorithmic Recourse provides recommendations to individuals who are adversely impacted by automated model decisions, on how to alter their profiles to achieve a favorable outcome. Effective recourse methods must balance three conflicting goals: proximity to the original profile to minimize cost, plausibility for realistic recourse, and validity to ensure the desired outcome. We show that existing methods train for these objectives separately and then search for recourse through a joint optimization over the recourse goals during inference, leading to poor recourse recommendations. We introduce GenRe, a generative recourse model designed to train the three recourse objectives jointly. Training such generative models is non-trivial due to lack of direct recourse supervision. We propose efficient ways to synthesize such supervision and further show that GenRe's training leads to a consistent estimator. Unlike most prior methods, that employ non-robust gradient descent based search during inference, GenRe simply performs a forward sampling over the generative model to produce minimum cost recourse, leading to superior performance across multiple metrics. We also demonstrate GenRe provides the best trade-off between cost, plausibility and validity, compared to state-of-art baselines. Our code is available at: https://github.com/prateekgargX/genre

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection schemes based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Diffusion models (DMs) have achieved record-breaking performance in image generation tasks. Nevertheless, in practice, the training-sampling discrepancy, caused by score estimation error and discretization error, limits the modeling ability of DMs, a phenomenon known as exposure bias. To alleviate such exposure bias and further improve the generative performance, we put forward a prompt learning framework built upon a lightweight prompt prediction model. Concretely, our model learns an anti-bias prompt for the generated sample at each sampling step, aiming to compensate for the exposure bias that arises. Following this design philosophy, our framework rectifies the sampling trajectory to match the training trajectory, thereby reducing the divergence between the target data distribution and the modeling distribution. To train the prompt prediction model, we simulate exposure bias by constructing training data and introduce a time-dependent weighting function for optimization. Empirical results on various DMs demonstrate the superiority of our prompt learning framework across three benchmark datasets. Importantly, the optimized prompt prediction model effectively improves image quality with only a 5\% increase in sampling overhead, which remains negligible.

Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works (Chen et al., 2023c;b; Benton et al., 2023; Lee et al., 2022) have analyzed algorithms for diffusion sampling with provable guarantees; these works show that for essentially any data distribution, one can approximately sample in polynomial time given a sufficiently accurate estimate of its score functions at different noise levels. In this work, we propose a new scheme inspired by Shen and Lee's randomized midpoint method for log-concave sampling (Shen & Lee, 2019). We prove that this approach achieves the best known dimension dependence for sampling from arbitrary smooth distributions in total variation distance ($\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work). We also show that our algorithm can be parallelized to run in only $\widetilde O(\log^2 d)$ parallel rounds, constituting the first provable guarantees for parallel sampling with diffusion models. As a byproduct of our methods, for the well-studied problem of log-concave sampling in total variation distance, we give an algorithm and simple analysis achieving dimension dependence $\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work.

Diffusion models, the most popular generative paradigm so far, can inject conditional information into the generation path to guide the latent towards desired directions. However, existing text-to-image diffusion models often fail to maintain high image quality and high prompt-image alignment for those challenging prompts. To mitigate this issue and enhance existing pretrained diffusion models, we mainly made three contributions in this paper. First, we propose **diffusion self-reflection** that alternately performs denoising and inversion and demonstrate that such diffusion self-reflection can leverage the guidance gap between denoising and inversion to capture prompt-related semantic information with theoretical and empirical evidence. Second, motivated by theoretical analysis, we derive Zigzag Diffusion Sampling (Z-Sampling), a novel self-reflection-based diffusion sampling method that leverages the guidance gap between denosing and inversion to accumulate semantic information step by step along the sampling path, leading to improved sampling results. Moreover, as a plug-and-play method, Z-Sampling can be generally applied to various diffusion models (e.g., accelerated ones and Transformer-based ones) with very limited coding and computational costs. Third, our extensive experiments demonstrate that Z-Sampling can generally and significantly enhance generation quality across various benchmark datasets, diffusion models, and performance evaluation metrics. For example, DreamShaper with Z-Sampling can self-improve with the HPSv2 winning rate up to **94%** over the original results. Moreover, Z-Sampling can further enhance existing diffusion models combined with other orthogonal methods, including Diffusion-DPO. The code is publicly available at [github.com/xie-lab-ml/Zigzag-Diffusion-Sampling](https://github.com/xie-lab-ml/Zigzag-Diffusion-Sampling).

Diffusion models have a tendency to exactly replicate their training data, especially when trained on small datasets. Most prior work has sought to mitigate this problem by imposing differential privacy constraints or masking parts of the training data, resulting in a notable substantial decrease in image quality. We present CPSample, a method that modifies the sampling process to prevent training data replication while preserving image quality. CPSample utilizes a classifier that is trained to overfit on random binary labels attached to the training data. CPSample then uses classifier guidance to steer the generation process away from the set of points that can be classified with high certainty, a set that includes the training data. CPSample achieves FID scores of 4.97 and 2.97 on CIFAR-10 and CelebA-64, respectively, without producing exact replicates of the training data. Unlike prior methods intended to guard the training images, CPSample only requires training a classifier rather than retraining a diffusion model, which is computationally cheaper. Moreover, our technique provides diffusion models with greater robustness against membership inference attacks, wherein an adversary attempts to discern which images were in the model's training dataset. We show that CPSample behaves like a built-in rejection sampler, and we demonstrate its capabilities to prevent mode collapse in Stable Diffusion.

Learning complex robot behavior through interactions with the environment necessitates principled exploration. Effective strategies should prioritize exploring regions of the state-action space that maximize rewards, with optimistic exploration emerging as a promising direction aligned with this idea and enabling sample-efficient reinforcement learning. However, existing methods overlook a crucial aspect: the need for optimism to be informed by a belief connecting the reward and state. To address this, we propose a practical, theoretically grounded approach to optimistic exploration based on Thompson sampling. Our approach is the first that allows for reasoning about _joint_ uncertainty over transitions and rewards for optimistic exploration. We apply our method on a set of MuJoCo and VMAS continuous control tasks. Our experiments demonstrate that optimistic exploration significantly accelerates learning in environments with sparse rewards, action penalties, and difficult-to-explore regions. Furthermore, we provide insights into when optimism is beneficial and emphasize the critical role of model uncertainty in guiding exploration.

Among the many variants of graph neural network (GNN) architectures capable of modeling data with cross-instance relations, an important subclass involves layers designed such that the forward pass iteratively reduces a graph-regularized energy function of interest. In this way, node embeddings produced at the output layer dually serve as both predictive features for solving downstream tasks (e.g., node classification) and energy function minimizers that inherit transparent, exploitable inductive biases and interpretability. However, scaling GNN architectures constructed in this way remains challenging, in part because the convergence of the forward pass may involve models with considerable depth. To tackle this limitation, we propose a sampling-based energy function and scalable GNN layers that iteratively reduce it, guided by convergence guarantees in certain settings. We also instantiate a full GNN architecture based on these designs, and the model achieves competitive accuracy and scalability when applied to the largest publicly-available node classification benchmark exceeding 1TB in size. Our source code is available at https://github.com/haitian-jiang/MuseGNN.

Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses suggest that DPS accomplishes posterior sampling by approximating the conditional score. While in this paper, we demonstrate that the conditional score approximation employed by DPS is not as effective as previously assumed, but rather aligns more closely with the principle of maximizing a posterior (MAP). This assertion is substantiated through an examination of DPS on 512$\times$512 ImageNet images, revealing that: 1) DPS’s conditional score estimation significantly diverges from the score of a well-trained conditional diffusion model and is even inferior to the unconditional score; 2) The mean of DPS’s conditional score estimation deviates significantly from zero, rendering it an invalid score estimation; 3) DPS generates high-quality samples with significantly lower diversity. In light of the above findings, we posit that DPS more closely resembles MAP than a conditional score estimator, and accordingly propose the following enhancements to DPS: 1) we explicitly maximize the posterior through multi-step gradient ascent and projection; 2) we utilize a light-weighted conditional score estimator trained with only 100 images and 8 GPU hours. Extensive experimental results indicate that these proposed improvements significantly enhance DPS's performance. The source code for these improvements is provided in https://github.com/tongdaxu/Rethinking-Diffusion-Posterior-Sampling-From-Conditional-Score-Estimator-to-Maximizing-a-Posterior.

Analog dynamical accelerators (DXs) are a growing sub-field in computer architecture research, offering order-of-magnitude gains in power efficiency and latency over traditional digital methods in several machine learning, optimization, and sampling tasks. However, limited-capacity accelerators require hybrid analog/digital algorithms to solve real-world problems, commonly using large-neighborhood local search (LNLS) frameworks. Unlike fully digital algorithms, hybrid LNLS has no non-asymptotic convergence guarantees and no principled hyperparameter selection schemes, particularly limiting cross-device training and inference. In this work, we provide non-asymptotic convergence guarantees for hybrid LNLS by reducing to block Langevin Diffusion (BLD) algorithms. Adapting tools from classical sampling theory, we prove exponential KL-divergence convergence for randomized and cyclic block selection strategies using ideal DXs. With finite device variation, we provide explicit bounds on the 2-Wasserstein bias in terms of step duration, noise strength, and function parameters. Our BLD model provides a key link between established theory and novel computing platforms, and our theoretical results provide a closed-form expression linking device variation, algorithm hyperparameters, and performance.

Recent advances in knowledge distillation (KD) have enabled smaller student models to approach the performance of larger teacher models. However, popular methods such as supervised KD and on-policy KD, are adversely impacted by the knowledge gaps between teacher-student in practical scenarios. Supervised KD suffers from a distribution mismatch between training with a static dataset and inference over final student-generated outputs. Conversely, on-policy KD, which uses student-generated samples for training, can suffer from low-quality training examples with which teacher models are not familiar, resulting in inaccurate teacher feedback. To address these limitations, we introduce Speculative Knowledge Distillation (SKD), a novel approach that leverages cooperation between student and teacher models to generate high-quality training data on-the-fly while aligning with the student's inference-time distribution. In SKD, the student proposes tokens, and the teacher replaces poorly ranked ones based on its own distribution, transferring high-quality knowledge adaptively. We evaluate SKD on various text generation tasks, including translation, summarization, math, and instruction following, and show that SKD consistently outperforms existing KD methods across different domains, data sizes, and model initialization strategies.