NeurIPS 2026 Papers

Guidance methods are essential tools for steering the generation process in diffusion models, improving the generalizability of stochastic robotic controllers and enabling high-quality controlled image synthesis. Despite strong parallels between flow-matching and diffusion, integrating guidance into flow-matching models remains quite challenging. Recent work has proposed general guidance frameworks for flow-matching, however, they are direct adaptations of diffusion guidance methods and can prove unstable. In this work, we conduct a theoretical analysis of guidance in flow-matching and show that a naive translation of diffusion-based guidance to flow-matching breaks the coupling distribution used during training, resulting in weaker control over sampling accuracy. Building on this insight, we propose **Coupled Guidance**, a flow-matching-specific guidance mechanism derived from a geometric perspective that leverages the coupling structure inherent to flow-matching training. To validate the effectiveness of our approach, we conduct extensive experimentation on a custom robotic *collision avoidance* task using Maniskill3, four robotic *dexterous manipulation* tasks from the Adroit benchmark, and three image generation tasks, namely *inpainting*, *super-resolution*, and *deblurring*, using the ImageNet-128 and CelebA-HQ-256 datasets. Our findings show that our framework improves sample quality and guidance stability across all tasks, without imposing any additional overhead.

Lane and road markings provide critical guidance for vehicle navigation and multi-agent coordination, yet their design principles are scattered across disparate datasets, severely limiting quantitative analysis and scenario testing. We introduce controllable road-marking generation: given a drivable-area mask and a sparse outer-ring observation, a model must synthesize a complete center-region layout of lane dividers, road dividers, and pedestrian crossings that is semantically consistent with a free-form text prompt. We develop a conditional diffusion pipeline that combines (i) a text-conditioned BEV diffusion backbone, (ii) a Gaussian blur-then-deblur training target that stabilizes thin-structure learning, and (iii) a structured Gaussian render post-processing step that snaps soft predictions to crisp, topology-aware markings. On the Argoverse 2 test split, our system substantially outperforms a state-of-the-art DDIM mask-refinement baseline on standard structural fidelity metrics, and supports prompt-level edits across crosswalk, lane-divider, and road-divider semantics. We anticipate that the proposed framework will enable downstream applications in urban infrastructure planning, autonomous-driving stress-testing, and navigation in unstructured environments.

In the classical *identification in the limit* model of Gold [Inf. Control, 1967], a stream of positive examples is presented round by round, and the learner must eventually recover the target hypothesis. Recently, Kleinberg and Mullainathan [NeurIPS 2024] introduced *generation in the limit*, where the learner instead must eventually output novel elements of the target's support. Both lines of work focus on positive-only or fully labeled data. Yet many natural supervision signals are inherently relational rather than singleton: comparative experiments, A/B tests, side-by-side judgments, and similarity–dissimilarity annotations produce observations that encode relationships between examples rather than labels of individual ones. This motivates us to initiate the learning-theoretic study of *contrastive identification and generation in the limit*, where the learner observes a *contrastive presentation* of data: a stream of unordered pairs $\\{x,y\\}$ satisfying $h(x)\ne h(y)$ for an unknown target binary hypothesis $h$, but which element is positive is hidden from the learner. We first present three results in the noiseless setting: an exact characterization of contrastive identifiable classes (a one-line geometric refinement of Angluin's tell-tale condition [Angluin, Inf. Control 1980]), a combinatorial dimension called *contrastive closure dimension* extending the closure dimension of Raman et al. [COLT 2025] and exactly characterizing uniform contrastive generation with tight sample complexity, and a strict hierarchy in which contrastive generation and text identification are mutually incomparable. We then prove a sharp *reversal* under finite adversarial corruption: there exist classes identifiable from contrastive pairs under any finite corruption budget by a single budget-independent algorithm, yet not identifiable from positive examples under even one corrupted observation. The unifying technical object is the *common crossing graph*, which encodes pairwise ambiguity, family-level generation obstructions, and corruption defects in a single coverage-and-incidence language.

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules---such as GANs or reward models---to restore visual fidelity. _In this work, we introduce **C**ontinuous-Time **D**istribution **M**atching (**CDM**), migrating the DMD framework from discrete anchoring to continuous optimization for the first time._ CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives.

Existing conditional diffusion models typically inject condition information into the reverse-time denoising process, either as model inputs or through guidance. Although effective for conditional fidelity, this design burdens the denoiser when compact continuous signals, such as user preference ratios or mixture degrees, must support both image reconstruction and condition-wise separation, often degrading sample quality. In this work, we reinterpret this limitation not as a problem of condition representation, but as a problem of condition placement. We propose the Continuous Personalized Diffusion Model (CPDM), which shifts the locus of conditioning from reverse-time signal injection to forward geometry formation by coupling bounded spinor-component coordinates with normalized image-space drift directions. The resulting condition-dependent forward drift forms condition-specific terminal geometry, from which continuous changes along the spinor-component coordinate are reflected as continuous visual transitions rather than endpoint interpolation. Experiments show that, even with a single scalar condition, CPDM achieves competitive performance compared with standard and higher-capacity reverse-conditioning baselines and supports continuous generation under compact scalar control. These results suggest forward geometry design as a practical alternative to conventional reverse-time conditioning for compact continuous personalization.

Real-world image degradation is often unknown, spatially non-uniform, and compositional, requiring all-in-one restoration models to adapt a single set of weights to diverse local corruption patterns without test-time degradation labels. Existing methods typically modulate a shared backbone with global prompts or degradation descriptors, or route features through predefined expert pools. However, compact global conditioning can bottleneck localized degradation evidence, while static expert routing may produce homogeneous updates or rely on unstable sparse assignments. We propose \textbf{Continuous Expert Assembly} (CEA), a token-wise dynamic parameterization framework for all-in-one image restoration. CEA employs a lightweight \textbf{Cross-Attention Hyper-Adapter} to probe intermediate spatial features and synthesize instance-conditioned low-rank routing bases and residual directions. Each spatial token then assembles its own residual update via dense signed dot-product affinities over the generated rank-wise components, avoiding external prompts, static expert banks, and discrete Top-$K$ selection. The resulting assembly rule also admits a linear-attention perspective, making its dense token-wise routing behavior transparent. Experiments on AIO-3, AIO-5, and CDD-11 show that CEA improves average restoration quality over strong prompt-, descriptor-, and expert-based baselines, with the clearest gains on spatially varying and compositional degradations, while maintaining favorable parameter, FLOP, and runtime efficiency.

Flow Matching enables high-quality visual generation via continuous-time dynamics, but inference remains costly due to multiple sequential function evaluations. Existing acceleration methods reduce the number of function evaluations but often introduce additional training overhead, degrade quality, or fail to account for input-dependent variability. We propose an inference-time method, CoFlow, that adaptively selects the step counts for each generation based on the prompt features. Our context-aware CoFlow is trained online with an unsupervised reward that balances efficiency and fidelity. Our method is plug-and-play, requiring no retraining of the generative model. It generalizes to image and video generation, achieving over $2.5\times$ speedup while preserving perceptual and semantic quality. We also provide theoretical insights into the link between adaptive step allocation and discretization error. The anonymized source code is available at \url{https://anonymous.4open.science/r/Contextual_Flow_Matching-9970}.

Standard Flow Matching (FM) models typically employ a pointwise loss function, effectively assuming that the velocity vector at each spatial position is pointwise decomposed supervision given the conditioning. We argue that this Pointwise Independence Assumption is suboptimal for image generation, where strong local correlations exist across space. Neglecting these dependencies leads to artifacts such as structural inconsistency. In this paper, we introduce Contextual Flow Matching (CFM), a generalized framework that enforces consistency not just on individual pixels, but on the contextual relationships within the velocity field. We formulate the training objective using a set of generalized Context Operators---akin to convolution kernels---that abstract relationship constraints. Specifically, we instantiate a Differential Operator to capture high-frequency motion dynamics and an Aggregate Operator to stabilize low-frequency structural evolution. Extensive experiments on ImageNet demonstrate that CFM significantly accelerates convergence and enhances generation fidelity by explicitly modeling spatial dependencies.

Autoregressive image generation has recently emerged as a competitive visual generation paradigm, yet its generation order is often predefined or heuristic, such as next-patch prediction, random-order prediction, or one-step generation for specific scales. We observe that these strategies can cause models to overlook important structural dependencies in images, thereby limiting both structural robustness and reasoning capability. In this work, we propose a context-aware autoregressive generation framework, where the model dynamically determines the next token location based on global context and current local information. Rather than following a fixed or random order, our method allows the generation process to adapt to image structure and semantic dependencies. Extensive experiments show that context-aware generation significantly improves structural robustness across different image AR paradigms, including masked autoregressive and scale-wise autoregressive models. Beyond quantitative improvements, we further observe emerging reasoning properties: the model can better understand complex semantic instructions and generate images that more faithfully follow the given guidance. These findings suggest that generation order is a critical yet underexplored factor in image autoregressive modeling, and that context-aware decoding can unlock stronger reasoning-aware visual generation capabilities.

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.

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.

Post-training quantization degrades multimodal model capabilities unevenly, yet practitioners lack a principled way to predict which capabilities will collapse. We propose the **Computational Depth Principle** (CDP): end-to-end fidelity under quantization follows $\hat p^n$, where $n$ counts sequential precision-dependent operations and $\hat p$ is a per-architecture survival rate. Across four VLM families and diverse benchmarks spanning image understanding, image generation, video understanding, and video generation, we show that deeper reasoning tasks consistently degrade more steeply and that a single shallow probe predicts the full degradation ranking on held-out architectures. The same exponential form extends to image generation, where denoising step count plays the role of depth, and to video understanding, where longer temporal reasoning chains amplify losses. For video generation, spatial quality degrades more than temporal coherence, indicating that the dominant compounding axis is denoising depth rather than cross-frame coupling. A complementary distortion-to-information (D/I) flip ratio diagnoses quantization method effects, revealing that certain methods preserve near-baseline quality while others produce catastrophic collapses on specific architecture pairings that aggregate accuracy alone cannot detect. Module ablation localizes the sensitivity to the language backbone rather than the vision encoder. Together, depth and D/I convert full-suite evaluation into a two-probe screening protocol that surfaces the highest-risk capability gaps first.

Self-supervised Vision Transformers (ViTs) like DINO encode rich semantics, enabling training-free segmentation of objects from the background and discovery of their parts via feature clustering. This paper focuses on part discovery: partitioning a foreground object into semantic parts. Existing approaches produce imprecise part boundaries. We trace this to the rigid ViT patch grid used in training DINO, where patches straddling boundaries contain pixels from multiple parts. While DINO's invariance-based training could absorb this pixel-level mixing into clean features, experiments with over 26K foreground patches show it does not: boundary-overlapping patches produce features with higher entropy and lower assignment confidence, blurring predicted part boundaries. Rather than make the massive effort of retraining DINO over geometrically coherent regions, an easier approach is to take boundaries directly from a boundary detector, which supplies the geometric information DINO's features lack. Motivated by this, we introduce Part-DINO, a training-free framework that combines boundaries from low-level image segmentation with DINO's semantic features. We use the boundaries to partition the image into regions, pool DINO features within each region, and group them to discover parts. Without any training, Part-DINO produces structurally coherent part assignments, outperforming training-free baselines across four standard benchmarks (CUB, CelebA, PartImageNet-OOD, PartImageNet-Seg) and remaining competitive with weakly-supervised and unsupervised methods.

Subject-driven generation (SDG) evaluation using multi-modal LLMs (MLLMs) provides better interpretability and stronger alignment with human judgment than traditional embedding-based methods. However, MLLM-as-a-Judge scores are limited in differentiating between error and error-free SDG images. In this paper, we propose CompJudge, which overcomes these limitations by introducing comparative capabilities to MLLM-as-a-Judge and recalibrating scores based on comparison results. To rigorously evaluate the correctness of SDG evaluators, we introduce CompILIAS, a diagnostic benchmark of triplets (reference, identity-preserving image, identity-degraded image) with verified binary ground-truth labels indicating whether the SDG image preserves the reference identity. We demonstrate improvements of SDG evaluation over existing approaches: 8.9pp on CompILIAS and 10.62--15.98pp on the DreamBench++ dataset. These improvements consistently generalize across diverse MLLM backbones and across subject categories.

Diffusion models achieve state-of-the-art image synthesis, with their generative trajectories fundamentally exhibit a spectral bias, resolving low-frequency global structures early and high-frequency fine details later. Conventional stochastic differential equation (SDE) solvers fail to account for this dynamic, naively injecting uniform white noise throughout the entire process and misusing the finite energy budget. In this work, we establish a mathematical framework that reconsiders SDE inference as a targeted, frequency-decoupled energy transfer. Leveraging this framework, we introduce Colored Noise Sampling (CNS), a novel, training-free stochastic solver. Rather than injecting uniform white noise, CNS utilizes a dynamic, timestep- and frequency-dependent schedule that more-efficiently allocates injected energy toward structurally unresolved frequency bands. By actively exploiting the model's inherent spectral bias, CNS systematically steers the generated distribution toward the true data manifold. Extensive experiments demonstrate that CNS significantly outperforms standard ODE and SDE baselines as a strictly plug-and-play, inference-time sampler substitution across diverse architectures (SiT, JiT, FLUX). Compared to standard sampling on ImageNet-256, CNS achieves substantial unguided FID reductions, improving from 8.26 to 6.27 on SiT-XL/2, 32.39 to 26.69 on JiT-B/16, and 11.88 to 8.31 on JiT-H/16, while yielding consistent relative FID improvements with Classifier-Free Guidance.

Text-to-image (T2I) models have advanced considerably in generating high-quality images from textual descriptions. However, their ability to associate colors with concepts remains largely constrained to explicit color names or codes, while their capacity to handle implicit concepts, such as emotions and visual states, remains underexplored. To address this gap, we introduce ColorConceptBench, an expert-annotated benchmark that systematically evaluates color-concept associations through probabilistic color distributions. ColorConceptBench moves beyond explicit color specifications by examining how models interpret 1,281 implicit color concepts, grounded in 6,584 human annotations. Our evaluation of nine leading T2I models reveals that performance varies substantially across semantic categories, and models exhibit a significant lack of sensitivity to abstract semantics. These limitations persist even when applying classifier-free guidance scaling at inference time, suggesting that achieving human-like color understanding demands a shift in how models learn and represent implicit semantic meaning.

Stellarators are fusion energy devices that confine hot plasma using a carefully shaped magnetic field, and they are one of the most promising candidates in the race towards commercial fusion. Among the many systems that make up a stellarator, the electromagnetic coils generate the confining magnetic field. Their design is the key factor in deciding whether a stellarator can be practically engineered and cost‑effectively realized. Coilset design is an intrinsically complex problem: it does not admit either a closed or a unique solution, making it suitable for optimization. Coilset optimization is therefore at the heart of stellarator design: a coilset must accurately reproduce a target magnetic field while satisfying stringent engineering constraints on coil spacing, curvature, and length. Although recent datasets have accelerated progress on stellarator equilibria optimization, data-driven coilset design is limited by the lack of standardized datasets that pair target plasma configurations with engineering-aware coilsets. Here, we release a dataset (https://huggingface.co/datasets/proxima-fusion/coilstellaration) of 177,000 optimized stellarator coilsets targeting plasma configurations sampled from the publicly available ConStellaration dataset. For each configuration, we optimized coilsets to reproduce the magnetic field while satisfying a diverse set of engineering constraints. Alongside the dataset, we introduce a benchmark for conditional coilset generation: given a target plasma boundary and a set of engineering requirements, a model should produce a coilset that satisfies the engineering constraints while reproducing the target field. We provide reference code, evaluation scripts and baselines models trained on a subset of the provided data (https://github.com/proximafusion/coilstellaration). Beyond enabling better optimization initializations and one-shot coil design, our dataset provides a testbed for data-driven constrained optimization and for studying which plasma geometry features predict simpler, more engineerable coils. By releasing data, and code for benchmarks and baselines, we aim to lower the barrier for machine learning and optimization researchers to engage with stellarator coilset design and accelerate progress toward engineerable and cost-effective stellarators power plants.

Selective state-space models (SSMs) have recently shown strong potential for efficient image restoration. A central difficulty, however, is that a 2D feature map typically needs to be linearized into a 1D token sequence for causal state-space updates, making restoration performance highly sensitive to the imposed scan order. Existing deterministic scans follow space-filling principles but remain fixed and content-agnostic, and can yield fragmented or semantically inconsistent contexts under degradations. We propose **CoScan**, a **co**ntent-adaptive **scan**-order design for causal vision SSMs. CoScan learns image-dependent space-filling traversals via differentiable proxy supervision driven by **scan-quality objectives** that encourage *short-range coherence and causal predictability, while preserving spatial adjacency*. To support hierarchical restoration backbones, we introduce an **efficient multi-scale scan construction** by *coarsening a fine-level minimum spanning tree*, producing coherent scans across feature resolutions. In addition, **a frequency-guided start selection strategy** is designed to *place informative structures early in the sequence prefix to strengthen causal context formation*. Plugged into existing Mamba-based backbones, CoScan yields consistent improvements across several restoration benchmarks with minimal overhead and shows promising results on high-level vision tasks. Code will be released upon acceptance.

We introduce CoLa3D, a simple and effective model for composable 3D scene decomposition that, given a single whole-scene latent from either a single image or an existing scene mesh as input, directly outputs a set of object meshes with consistent spatial layout that can be assembled back into a coherent scene. CoLa3D introduces a novel paradigm for 3D scene decomposition within a shared \emph{whole}-scene latent, unlike alternatives that perform per-object generation in canonical spaces and then glue the objects back together with fragile pose and scale estimation. The network is a lightweight, flexible, and scalable query-based transformer that accepts various types of queries, including 2D masks, 3D points, and learnable queries, and learns to decompose the scene into objects in a compact latent space. On both synthetic and real-world datasets, CoLa3D achieves state-of-the-art performance on composable 3D scene decomposition, substantially improving global scene-level consistency and object-level quality while running $2\times$ faster and using less than 1% of SAM 3D's training data. Visible depth on par with MoGe2 further confirms that latent decomposition preserves accurate visible scene geometry while producing physically complete, decomposable object meshes.