ICML 2026 Papers

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks (lrRNNs) to infer low-dimensional latent dynamics and connectivity from observed activity, enabling a mechanistic interpretation of the dynamics. However, standard approaches for training lrRNNs can recover spurious structures irrelevant to the underlying dynamics. We first characterize the identifiability of connectivity structures in lrRNNs and determine conditions under which a unique solution exists. To find such solutions, we develop an inference framework based on maximum entropy and continuous normalizing flows (CNFs), trained via flow matching. Instead of estimating a single connectivity matrix, our method learns a distribution over connection weights that is maximally unbiased over unidentifiable components while matching the observed dynamics. This approach captures complex yet necessary distributions such as heavy-tailed connectivity found in empirical data. We validate our method on synthetic datasets with connectivity structures that generate multistable attractors, limit cycles, and ring attractors, and demonstrate its applicability in recordings from rat frontal cortex during decision-making. Our framework shifts circuit inference from recovering connectivity to identifying which connectivity structures are computationally required, and which are artifacts of underconstrained inference.

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically bifurcate into inverse methods, which struggle with the ill-posed nature of mapping scores to designs, and forward methods, which often lack the distributional expressivity to quantify uncertainty effectively. In this work, we propose \textbf{SPADE} (\textbf{S}upport-\textbf{P}roximity \textbf{A}ugmented \textbf{D}iffusion \textbf{E}stimation), a novel framework that reimagines forward surrogate modeling through the lens of conditional generative modeling. SPADE models the forward likelihood $p(y|\boldsymbol{x})$ using a diffusion model, but with two critical enhancements to tailor it for optimization: (1) a \emph{Calibrated Diffusion Estimation} module that enforces global consistency in statistical moments and pairwise rankings, and (2) a \emph{Support-Proximity Regularization} mechanism that implicitly internalizes the data manifold constraint $p(\boldsymbol{x})$ via kNN-based density estimation. Theoretically, we prove that our regularization is first-order equivalent to maximizing a Bayesian posterior with a valid design prior. Empirically, SPADE achieves state-of-the-art performance across Design-Bench tasks and an LLM data mixture optimization benchmark. Our code is available at https://github.com/HarryYoung2018/spade.

We present SemanticNVS, a camera-conditioned multi-view diffusion model for novel view synthesis (NVS), which improves generation quality and consistency by integrating pre-trained semantic feature extractors. Existing NVS methods perform well for views near the input view, however, they tend to generate semantically implausible and distorted images under long-range camera motion, revealing severe degradation. We speculate that this degradation is due to current models failing to fully understand their conditioning or intermediate generated scene content. Here, we propose to integrate pre-trained semantic feature extractors to incorporate stronger scene semantics as conditioning to achieve high-quality generation even at distant viewpoints. We investigate two different strategies, (1) warped semantic features and (2) an alternating scheme of understanding and generation at each denoising step. Experimental results on multiple datasets demonstrate the clear qualitative and quantitative (4.69%-15.26% in FID) improvement over state-of-the-art alternatives.

Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: *the rapid decay of intra-group variance*. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into *premature stagnation or reward hacking*. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in *training instability or diminishing returns*. To overcome these challenges, we propose **$E$mbedding-perturbed $E$xploration Preference Optimization ($E^2$PO)**, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.

Graph generation is a fundamental task with broad applications, such as drug discovery. Recently, discrete flow matching-based graph generation, a.k.a., graph flow model (GFM), has emerged due to its superior performance and flexible sampling. However, effectively aligning GFMs with complex human preferences or task-specific objectives remains a significant challenge. In this paper, we propose Graph-GRPO, an online reinforcement learning (RL) framework for training GFMs under verifiable rewards. Our method makes two key contributions: (1) We derive an analytical expression for the transition probability of GFMs, replacing the Monte Carlo sampling and enabling fully differentiable rollouts for RL training; (2) We propose a refinement strategy that randomly perturbs specific nodes and edges in a graph, and regenerates them, allowing for localized exploration and self-improvement of generation quality. Extensive experiments on both synthetic and real datasets demonstrate the effectiveness of Graph-GRPO. With only 50 denoising steps, our method achieves 95.0\% and 97.5\% Valid-Unique-Novelty scores on the planar and tree datasets, respectively. Moreover, Graph-GRPO achieves state-of-the-art performance on the molecular optimization tasks, outperforming graph-based and fragment-based RL methods as well as classic genetic algorithms. Code is available in https://github.com/Zhubaoheng/Graph-GRPO.

Reliable epidemic forecasting is critical for public health decision-making yet remains challenging due to data sparsity and the non-stationary nature of disease dynamics. While recent hybrid models attempt to integrate mechanistic principles with data-driven approaches, they often relegate mechanistic priors to merely auxiliary features or regularization terms. This design not only obscures the interpretability of the mechanistic contribution but also fails to inherit the capability of physical models to generalize under non-stationary dynamics, as the core architecture remains predominantly data-driven. To address these limitations, we propose EpiDiff, a unified framework that synergizes epidemiological domain knowledge with the generative power of diffusion models. Unlike methods that rigidly fuse features, EpiDiff employs a novel uncertainty-aware steering mechanism during inference. Specifically, we quantify the posterior uncertainty of mechanistic estimations and use it to dynamically modulate the diffusion process. Extensive experiments on real-world datasets demonstrate that EpiDiff consistently outperforms state-of-the-art baselines in accuracy and robustness, particularly under non-stationary distributions, while offering transparent insights into model reliance by explicitly visualizing when the forecast is governed by mechanistic laws versus data-driven patterns.

Masked diffusion models (MDMs) are a potential alternative to autoregressive models (ARMs) for language generation, but generation quality depends critically on the generation order. Prior work either hard-codes an ordering (e.g., blockwise left-to-right) or learns an ordering policy for a pretrained MDM, which incurs extra cost and can yield suboptimal solutions due to the two-stage optimization. Motivated by this, we propose order-expressive masked diffusion model (OeMDM) for a broad class of diffusion generative processes with various generation orders, enabling the interpretation of MDM, ARM, and block diffusion in a single framework. Furthermore, building on OeMDM, we introduce learnable-order masked diffusion model (LoMDM), which jointly learns the generation ordering and diffusion backbone through a single objective from scratch, enabling the diffusion model to generate text in context-dependent ordering. Empirically, we confirm that LoMDM outperforms various discrete diffusion models across multiple language modeling benchmarks.

In contemporary deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a {\em distribution over PEFT parameters}. We then learn the downstream task by a {\em sample-and-evaluate} procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a {\em finite} set of PEFT samples. In contrast to the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

Text-to-image diffusion models achieve impressive visual fidelity, yet they remain unreliable in multi-object generation. Despite extensive empirical evidence of these failures, the underlying causes remain unclear. We begin by asking how much of this limitation arises from the data itself. To disentangle data effects, we consider two regimes across different dataset sizes: (1) concept generalization, where each individual concept is observed during training under potentially imbalanced data distributions, and (2) compositional generalization, where specific combinations of concepts are systematically held out. To study these regimes, we introduce mosaic (Multi-Object Spatial relations, AttrIbution, Counting), a controlled framework for dataset generation. By training diffusion models on mosaic, we find that scene complexity plays a dominant role rather than concept imbalance, and that counting is uniquely difficult to learn in low-data regimes. Moreover, compositional generalization collapses as more concept combinations are held out during training. These findings highlight fundamental limitations of diffusion models and motivate stronger inductive biases and data design for robust multi-object compositional generation.

With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM trajectory tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory trajectory tangents, we propose a new loss function, called the {\em manifold feature distance (MFD)}, which provides manifold-aligned trajectory tangents that point toward the data manifold. Consequently, our method -- dubbed {\em Align Your Trajectory Tangent (AYT)} -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality. Code is available at \url{https://github.com/1202kbs/AYT}

Discrete flow matching, a recent framework for modeling categorical data, has shown competitive performance with autoregressive models. However, unlike continuous flow matching, the rectification strategy cannot be applied due to the stochasticity of discrete paths, necessitating alternative methods to minimize state transitions. We propose a dynamic-optimal-transport-like minimization objective and derive its Kantorovich formulation for discrete flows with convex interpolants, where transport cost depends solely on inter-state dissimilarity and can be optimized via minibatch strategies. We show that such methods can reduce the number of transitions up to 32 times (1024 to 32) to reach the same generative perplexity without compromising diversity. Additionally, path nondeterminism in discrete flows precludes an instantaneous change-of-variables analogue, preventing precise probability estimation available to continuous flows. We therefore propose two upper bounds on perplexity, enabling principled training, evaluation and model comparison. Finally, we introduce Multimask Flows which outperform masked flows in generative perplexity without compromising diversity, particularly when utilizing minibatch Optimal Transport.

Personalization techniques for image generation models have increasingly been misused for malicious purposes, including unauthorized style imitation and copyrighted content replication. In response, recent mimicry protection methods embed carefully designed perturbations into images to disrupt a model’s ability to learn genuine semantic representations. Despite their growing adoption, the robustness of these protection mechanisms remains poorly understood, raising concerns about their reliability in real-world deployment. In this work, we present the first systematic analysis showing that DDIM inversion inherently acts as a perturbation amplifier, causing protected images to suffer severe structural distortions during reconstruction. Building on this observation, we propose DDIM Inversion-based Reconstruction Purification (DIRP), a novel purification approach that removes protective perturbations by explicitly minimizing DDIM inversion reconstruction error under perceptual constraints. Extensive experiments on six existing mimicry protection methods demonstrate that DIRP consistently outperforms five state-of-the-art attack baselines, achieving superior perturbation removal while better preserving image quality. Our results expose fundamental vulnerabilities in current mimicry protection strategies and highlight the urgent need for more robust and principled defenses.

Diffusion Language Models (DLMs) generate text by iteratively denoising a masked sequence, repeatedly deciding which positions to commit at each step. Standard decoding follows a greedy rule, unmasking the most confident positions, yet this local choice can lock the model into a suboptimal unmasking order, especially on reasoning-heavy prompts. We present Search Or AcceleRate (SOAR), a training-free decoding algorithm that adapts its behavior to the model’s uncertainty. When confidence is low, SOAR briefly widens the search over alternative unmasking decisions to avoid premature commitments; when confidence is high, it collapses the search and decodes many positions in parallel to reduce the number of denoising iterations. Across mathematical reasoning and code generation benchmarks (GSM8K, MBPP, HumanEval) on Dream-7B and LLaDA-8B, SOAR improves generation quality while maintaining competitive inference speed, offering a practical way to balance quality and efficiency in DLM decoding.

The abundance of pre-trained diffusion models provides an opportunity for composition. Combining several models, however, runs the risk of one model dominating or models disagreeing with each other. Here, we propose Divide-and-Denoise, a method for coordinating multiple pre-trained diffusion models during sampling. Much like managing a specialized workforce, our method creates a fair but efficient division of labor across models. Central to our method is the notion of an allocation which defines the responsibility of each model to every region of the noisy sample. At every timestep, we then denoise by (i) updating the allocation by solving a fair division game, where we divide the sample into regions that maximize total utility under fairness constraints, and (ii) aligning the models with this allocation, where we guide each model to denoise within its assigned region. This leads to a new composite denoising process that evolves in tandem with a division process. We evaluate Divide-and-Denoise on conditional image generation. Across several quality metrics, including the GenEval benchmark, our method outperforms baselines and resolves common failures including missing objects and mismatched attributes. Experiments show that Divide-and-Denoise utilizes each model's expertise without neglecting any other model.

This paper studies the theoretical foundations of guidance mechanisms in continuous-time score-based diffusion models. We adopt Doob’s h-transform as a principled framework for characterizing ideal guided diffusion processes and analyze the discrepancy between ideal and approximate guidance. Our analysis provides explicit error bounds and yields probabilistic guarantees on satisfying prescribed constraints, which are particularly important for safety-critical planning. We further show that the Doob-based formulation induces a stochastic optimal control problem, enabling practical guidance design without additional model training. We demonstrate the effectiveness of the proposed framework on robotic navigation tasks, including language-conditioned planning.

We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first and higher-order flow matching and ties model complexity to the intrinsic manifold dimension. Building on these, we establish tighter sample-complexity bounds for velocity approximation, velocity estimation, and distribution estimation. Our results show how flow-matching transformers escape the curse of dimensionality by utilizing intrinsic data structure.

Most federated recommender systems represent each user with a single embedding learned from local interaction data, implicitly assuming that user preferences are fixed and precisely identifiable. In federated settings, however, each client observes only a limited and fragmentary view of user behavior, rendering such point estimates inherently brittle. To address this mismatch, we model user preferences as distributions rather than points, allowing multiple compatible preference representations to coexist. Rather than collapsing evidence into a single embedding, our approach preserves uncertainty and diversity in user representations, providing a richer basis for preference modeling. We instantiate this idea with a diffusion-based generative framework that produces diverse user embeddings and derives recommendation scores by aggregating predictions across them. This distributional formulation yields more stable ranking behavior and improved robustness under ambiguous feedback. Extensive experiments on federated recommendation benchmark datasets demonstrate consistent and significant improvements over baselines. Our code is available.

Despite the central role of sensor-derived measurements such as imaging traits and plasma biomarkers in biomedical research and clinical practice, existing generative models for disease prediction largely depend on event-level representations from hospital and registry data. Given the multi-factorial nature of human disease, the absence of explicit modeling of social determinants of health (SDoH) limits the capacity for personalized disease modeling and clinical decision support. To address this limitation, we propose a generative model with ICD-coded proxies of SDoH for \textit{in silico} modeling of disease reasoning, a conditioned latent diffusion framework that establishes the connection between multi-organ sensor data with tokenized healthcare events. Specifically, we introduce a novel geometric diffusion model to characterize the temporal evolution of complex data representation such as brain networks (region-to-region connectivity encoded in a graph), in parallel with diffusion models for tabular data from other organ systems. Together, we integrate the generative model with digitalized SDoH proxies (coined **DiffDT**) for simulated intervention and reasoning of future disease trajectories. We conduct extensive experiments on the UK Biobank (UKB) dataset, which contains organ-specific imaging traits, including brain (44,834), heart (23,987), liver (28,722), and kidney (32,155), along with nearly 500k medical history sequences (age range: 25$\sim$89 years). Our **DiffDT** achieves significant improvements over state-of-the-art human disease autoregressive models and imaging trait generative baselines.

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models---two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal–dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.