NeurIPS 2026 Papers

Diffusion and flow models enable powerful generative modeling, but controlled editing remains challenging due to the need to balance source fidelity and edit compliance along the generative trajectory. We propose a principled, inversion-free framework for flow-based image editing from a trajectory centric perspective. Rather than relying on inversion or heuristic guidance, we introduce a one-step look-ahead mechanism that evaluates the effect of candidate updates on both edit and fidelity rewards estimated via denoising, and adjusts the current update based on this evaluation. At each step, our method applies reward-driven corrections guided by the look-ahead evaluation under an explicit fidelity constraint, resulting in stable and coherent trajectory evolution. This look-ahead design mitigates gradient interference between edit and fidelity objectives by anticipating their interaction in future states, leading to improved trade-offs. Experiments demonstrate that the proposed approach achieves stronger semantic edits while better preserving source content compared to existing strong baselines.

Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Constrained decoding is essential for serving LLMs, ensuring that generated outputs follow specific structures such as JSON schema-formatted function calls. Existing systems are designed for autoregressive models and assume left-to-right generation, masking out invalid next tokens at each step. Diffusion language models, however, break this assumption: they sample multiple positions simultaneously from a fully-factorized mean-field distribution at each denoising step. In this paper, we present an exact and tractable algorithm for sampling from the constrained mean-field posterior under any constraint expressible as a finite automaton. Viewing finite automata as graphical models, we obtain tractable representations of the constrained distribution that enable efficient inference. The approach guarantees constraint satisfaction by construction, supports both greedy and sampling-based decoding, and is compatible with parallel and block-wise decoding under arbitrary remasking schedules. Applying depth-reduction techniques from arithmetic circuit theory, we further reduce sampling depth from linear to logarithmic in the sequence length. Empirical evaluations on Dream-7B and LLaDA-8B show substantial accuracy gains across various tasks including function calling (xLAM, BFCL), planning (Sudoku, Countdown), text-to-SQL (Spider), and math reasoning (GSM-Symbolic), with little inference overhead relative to unconstrained decoding. For example, on BFCL-Live, our approach improves Dream-7B's greedy decoding accuracy from 63.9% to 71.5%, and stochastic sampling accuracy from 22.3% to 69.0%, where the unconstrained baseline collapses, with under 5% wall-clock overhead.

Determinantal point processes allow efficient sampling of diverse subsets of data. However, (exact) sampling under additional constraints is often computationally intractable under complexity-theoretic assumptions. We take an algebraic approach to designing novel algorithms that allow exact constrained sampling with theoretical efficiency guarantees. Our algorithms apply to a general class of point processes based on Bombieri inner products of polynomials, which we call Bombieri $k$-point processes. This perspective recovers known algorithms for constrained $k$-DPPs and extends them to a broader class of simple $k$-point processes. As applications, we obtain exact samplers for matching-, path-, subgraph-, and budget-constrained processes, as well as distributions combining diversity with clustering. While common complexity-theoretic assumptions rule out polynomial-time algorithms in many of these settings, our algorithms are efficient with respect to the relaxed notion of fixed-parameter tractability when the sample size $k$ is kept bounded.

Post-training of language models is commonly framed as a sample-score-update loop implemented by gradient descent. A recent line of work, exemplified by RandOpt, relocates this loop to weight space, sampling Gaussian perturbations around a pretrained model and ensembling the top-$K$ rewarded specialists at inference. While competitive with PPO and GRPO under matched training compute, this prediction-level ensemble incurs $K$ forward passes per test example and does not extend cleanly to free-form generation. We ask whether the rewarded population can instead be folded into a single deployable model, replacing the inference-time ensemble with one consolidated update. A split-half analysis over 25 model-task pairs reveals reproducible low-rank structure in every case. We turn this geometry into CoRP (Consolidating Rewarded Perturbations), a gradient-free operator that combines reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate, with no gradient flowing through the language model. Across five language models from $0.5$B to $8$B and five tasks covering math, code, and creative writing, CoRP improves the base model by $8.1$ points on average. Using one tenth of RandOpt's perturbation budget, CoRP exceeds single-inference RandOpt by $6.5$ points and recovers more than half of the gain of the 50-pass majority-vote ensemble, at one forward pass per test example.

Parallel thinking scales inference-time compute by generating multiple reasoning traces for a query, and aggregating them to reach a final answer. However, most aggregation algorithms treat each reasoning trajectory independently, ignoring the complementary reasoning sub-processes across the full ensemble of trajectories. To learn from these parallel trajectories, we propose CORAL (Consolidating Reasoning with Test-Time Learning), a novel framework for aggregating trajectories by jointly consolidating them into parametric memory using test-time training. Our algorithm meta-learns how to consolidate using nested optimization at training time, where an inner loop encodes reasoning trajectories into a lightweight LoRA adapter, and an outer loop learns meta-parameters for the inner loop such that the consolidation is helpful for the model to synthesize a final solution. As no standard datasets exist for training aggregation methods, we construct a novel OpenParallelThinking corpus composed of 12,810 math problems paired with a mixture of diverse trajectories from six LLMs. Evaluated on challenging mathematics and STEM benchmarks, CORAL consistently outperforms best aggregation baselines by 20% overall. Importantly, we curate reasoning trajectories at multiple quality levels to simulate the reality of noisy parallel reasoning and demonstrate that CORAL is especially robust to the quality of thinking trajectories and able to learn useful knowledge from entirely wrong solutions. Additionally, this weak-to-strong generalization feature scales with the number of incorrect trajectories available for aggregation, while RL can further incentivize such reasoning consolidation capability. We will release CORAL and OpenParallelThinking for use in future work on reasoning aggregation.

Federated graph learning (FGL) enables privacy-preserving collaborative training over distributed graph data, yet remains vulnerable to backdoor attacks from malicious clients. In FGL, data and structural heterogeneity make benign clients difficult to distinguish from malicious ones, posing a key challenge to reliable defense. We propose VeriDrift, a backdoor defense framework for FGL based on cross-layer drift and consistency verification. On the client side, VeriDrift derives a client-level risk score from node-level cross-layer drift anomalies during GNN propagation. On the server side, VeriDrift verifies the consistency between the reported risk and the submitted model update, and converts the resulting verified risk into aggregation weights to suppress suspicious updates. Without relying on auxiliary clean data, VeriDrift enables reliable risk assessment under heterogeneous FGL and improves robustness against adaptive attacks. Extensive experiments show that VeriDrift consistently reduces attack success rates across different FGL backdoor settings while maintaining clean accuracy.

Test-time scaling often uses an external verifier, such as compilers and test-cases in coding or trained value functions in robotics application, to obtain high quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because in many real-world applications we do not have access to such high quality verifiers. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and data. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. We introduce KL-based metrics for miscoverage and miscalibration, and use these to show that the DRO-NPE objective controls overfitting and reduces posterior overconfidence. Our method is tractable, parallelisable, and readily integrates with standard normalising flows. Across benchmark SBI tasks, DRO-NPE consistently improves coverage and calibration, while narrowing the gap between empirical and population NPE loss, leading to more reliable inference in low-simulation regimes.

Offline multi-objective optimization aims to identify high-quality trade-off designs using only a fixed dataset of previously evaluated candidates. Existing methods often cast this problem as guided generative sampling, producing a finite candidate pool by steering a diffusion or flow model toward Pareto-preferred regions. We study a different interface: deterministic Pareto set amortization. Our method, Offline Pareto Set Learning (OffPSL), trains a preference-conditioned map $h_\pi:\Delta^{m-1}\rightarrow \mathcal{X}$ that returns one design for each requested trade-off direction. Because offline data contain no preference–solution labels, OffPSL trains this map using two offline-only signals: a coordinate-wise pessimistic surrogate scalarization and a diffusion-style denoising-residual support regularizer learned from offline designs. The denoising model is used only as a frozen support prior and is not used to sample candidates. At inference, OffPSL produces exactly one candidate per reference direction with no iterative sampling, test-time optimization, or filtering from a larger generated pool. On standard offline MOO benchmarks, OffPSL is competitive with recent guided generative baselines while keeping the learned preference-to-design map directly queryable and diagnosable.

We propose a conservative continuous-time stochastic control framework for treatment optimization from irregularly sampled patient trajectories. We model the unknown patient dynamics as a controlled stochastic differential equation where treatment is a continuous-time control input. Naive model-based optimization can exploit model errors and propose out-of-distribution controls that appear optimal under the learned model but perform poorly under the true dynamics. To mitigate such extrapolation, we introduce a consistent, signature kernel MMD regularizer on path space, which penalizes controls whose predicted trajectories deviate from observed ones. The resulting conservative objective minimizes a tractable upper bound on the true cost. Experiments on pharmacometric simulators show improved robustness and performance compared to non-conservative baselines.

Learning constraint-satisfying policies from offline data without risky online interaction is crucial for reliable deployment of reinforcement learning (RL) agents. Representative methods leverage Implicit Q-Learning and advantage-weighted regression to learn value functions and balance the reward–safety trade-off, demonstrating solid safety performance in safety-critical hard constraint scenarios. However, these methods typically couple reward and safety optimization during offline training and rely on a predefined unified factor to balance the reward–safety trade-off (conservatism). Which ignores the fact that different tasks, due to their distinct reward and cost functions, may require different degrees of conservatism to satisfy safety constraints, resulting in sub-optimal performance. To address this limitation, we propose Co3G, a compositional generative model with test-time controllable conservatism for offline safe RL. During training, Co3G decouples the optimization objectives by separately employing reward-optimal guidance and safety-optimal guidance to induce high-reward and high-safety actions. During deployment, Co3G combines the reward and safety objectives via compositional generation, and further provides three mechanisms—manual tuning, rejection sampling, and RL—to balance the reward and safety guidance scales during deployment, thereby achieving a superior reward–safety trade-off. Extensive experiments on the OSRL benchmark show that Co3G delivers strong safety performance under stringent safety constraints while retaining flexible control over conservatism, significantly outperforming previous hard-constraint and soft-constraint baselines.

While autoregressive models optimize the exact likelihood implied by the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--model cross-entropy (CE) can be characterized \emph{exactly} as an integral of \emph{local} information-theoretic derivatives along the noise path. This yields a unified characterization of the likelihood for discrete diffusion and continuous diffusion, with the Gaussian case reducing to the well-known I-MMSE relationship connecting mutual information and estimation theory. An immediate implication is a \emph{locality} property: one can compute the information-theoretic derivatives using only the marginal posteriors along the noise path. As a result, training reduces to learning the marginal posteriors by minimizing the negative log-likelihood. While the conservation law implies that the entropy does not depend on the noise path, finite-capacity denoisers approximate the posteriors with varying accuracy across noise types, leading to differences in performance. We validate these predictions on synthetic Markov sources and standard benchmarks, including \texttt{text8} and CIFAR-10.

Federated Learning (FL) enables collaborative model training across clients while preserving data privacy. However, FL typically relies on voluntary client participation with uniform rewards, which can lead to high-quality clients dropping out due to inadequate incentives and low-quality clients taking a free-ride, both of which degrade overall model performance. However, existing incentive mechanisms fail to capture the true contribution value of a client’s data to the global model, and often skew client selection toward cost compression rather than quality enhancement, thereby exacerbating confounding bias. To address this, we propose CausalAFL, a causal-based framework that reduces information asymmetry and corrects for confounding factors. Specifically, CausalAFL builds a complete causal chain connecting client information, bid, and marginal contribution. By jointly optimizing an inference network and a generative network within a variational inference framework, it precisely adjusts for causal bias. Maximizing the evidence lower bound objective allows CausalAFL to separate true contribution from noise and highlight the value of high-quality clients. A social welfare objective that quantifies both natural direct and indirect effects guides the server to prioritize these clients, resulting in improved global model accuracy and social welfare. Experiments on multiple datasets demonstrate that CausalAFL can guide clients to adjust their bids, leading to winners with higher contributions, confirming its effectiveness.

A local specialist LLM, fine-tuned with reinforcement learning from verifiable rewards (RLVR) on operator-local data, is installed inside a single regulated organization under a per-deployment error budget $\alpha$. The operator needs a safety certificate that holds on *this* deployment's stream, simultaneously at every wall-clock round: no pooling across deployments, no waiting for a long-run average. Existing wrappers cannot deliver this on these adaptive, online-updated streams: offline conformal-risk methods require exchangeability; online-conformal methods bound only long-run averages; non-exchangeable extensions are marginally valid; and the closest anytime wrapper, A-RCPS, controls marginal rather than selective risk. Through a (test statistic, validity guarantee, deployment rule) framework we identify one empty cell forced by the deployment requirements (e-process per threshold, selective risk, anytime-pathwise validity, max-certified-threshold rule); **Conformal Selective Acting** (CSA) fills it as a per-round wrapper maintaining a Ville-type e-process per candidate score threshold on a Bonferroni grid, evaluated against the RLVR filtration. Under predictable updates and isotonic-calibrated monotone risk we prove (i) an anytime-pathwise selective-risk bound $R_T^{\mathrm{act}} \le \alpha + O(N_T^{-1/2})$, (ii) rate-optimal certification matching $\Theta(\bar\eta^{-2} \log(1/\delta))$, and (iii) a horizon-independent release-rate gap. Across eight specialist benchmarks (480 streams), sixteen adversarial distribution-shift cells (160 streams), and five live Expert-Iteration RLVR cells with online LoRA over four base models in three architecture families (10,300 rounds), CSA is the only method among ten directly compared that satisfies both pathwise validity and non-refusing deployment on every cell. We do not propose a new LLM, training algorithm, or policy class; CSA is the deployment-side complement, orthogonal to the model itself, for operators who cannot use a frontier API.

Uncertainty quantification (UQ) for large language models (LLMs) aims to provide reliable measures of predictive confidence, yet current methods often fail to remain stable under simple, meaning-preserving perturbations. We identify an important source of instability: semantically equivalent paraphrases of the same input can induce substantial variability in predictive confidence, even for methods with formal guarantees such as conformal prediction. To address this issue, we propose a paraphrase-aware UQ framework that explicitly enforces invariance to semantic rewordings. Instead of relying on a single input, our approach constructs uncertainty scores by aggregating predictions across a set of its paraphrases, using a lightweight proxy model to produce calibrated and comparable outputs. This aggregation yields uncertainty estimates that are both more stable and more informative, while remaining compatible with conformal calibration techniques to retain coverage guarantees. Across multiple UQ benchmarks and model families, our method achieves nominal coverage with smaller and more stable prediction sets under paraphrase perturbations. Code is available at https://anonymous.4open.science/r/PA_Score-8C0D.

Uncertainty quantification is crucial in scientific machine learning, where models inform safety-critical tasks such as flood forecasting, financial risk management, and thermal control in machines. Conformal prediction provides distribution-free coverage guarantees, but in time-dependent settings common to physics and engineering, these guarantees can break down, leading to systematic undercoverage. We study this problem in the context of surrogate models for time-dependent physical systems described by partial differential equations. We prove that in a function space setting, distributions at arbitrarily close times can be mutually singular, making exact coverage guarantees impossible. We further show that in discretized settings, the total variation distance between distributions often grows exponentially with the grid resolution mandating restrictions on the spatial discretization to ensure coverage. Finally, for certain settings, we show how to use principled weighted conformal prediction to obtain finite-sample coverage guarantees over growing time horizons.

Conformal Prediction (CP) provides a model-agnostic framework for constructing finite-sample prediction sets with coverage guarantees and has become a tool for reliable decision-making in high-risk settings. Recent advances have extended Split Conformal Prediction to increasingly complex learning problems, including multilabel, high-dimensional, and functional outputs. In this work, we study CP for Distribution-to-Distribution Regression, a setting of growing interest across many application domains. We show that a naive application of Split CP yields prediction sets that, while marginally valid, are non-interpretable, e.g., lacking a well-defined volume or a tractable sampling procedure, and of limited practical value. To overcome this, we propose a new conformal framework that operates in an orthogonal basis space, producing interpretable prediction sets while preserving coverage guarantees. We further develop an adaptive variant with asymptotic conditional coverage under mild assumptions. Empirical results on synthetic and real-world datasets validate the effectiveness of the proposed approach.

While diffusion and flow-based generative models have achieved impressive performance in high-fidelity image and video synthesis, this capability comes at the cost of substantial inference overhead during iterative sampling. Cache-based acceleration alleviates this cost by reusing intermediate computations across adjacent denoising or transport steps, typically relying on lightweight proxy discrepancies to decide when cached outputs should be refreshed. However, such proxy-discrepancy rules are inherently unreliable: the proxy is only a point estimate of the inaccessible oracle discrepancy and can misalign across prompts, timesteps, and generation dynamics. This mismatch induces asymmetric failures: proxy underestimation may cause unsafe reuse of stale cached computations and degrade generation quality, while proxy overestimation leads to overly conservative refreshes and reduced acceleration. To address these issues, this paper introduces Conformal Cache, dubbed CCache, a training-free conformal calibration framework for reliable cache-based generation acceleration. Our key insight is to formulate cache reuse as a one-sided risk-control problem and adaptively calibrate a timestep-wise upper correction for the signed proxy-to-oracle gap based on split conformal prediction. CCache is plug-and-play and can be integrated with different proxy-discrepancy caching baselines without structural modifications or parameter updates to the generative model. Extensive experiments on image and video generation demonstrate that \methodname improves generation quality and cache reliability while preserving favorable speed-quality trade-offs.