NeurIPS 2026 论文列表

Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: distributions over probability measures on non-Euclidean domains. Existing generative methods largely assume Euclidean geometry and fail to capture this structure. We introduce Riemannian Wasserstein Entropic Flow Matching (RWEFM), a generative framework on the Wasserstein space $\mathcal{P}_2(\mathcal{M})$ of a Riemannian manifold $(\mathcal{M},g)$. RWEFM is trained by regressing a neural vector field onto Riemannian optimal transport velocities, using McCann displacement interpolations as conditional paths. We confirm theoretically that this construction leads to a valid flow matching approach on $\mathcal{P}_2(\mathcal{M})$ and introduce the Riemannian Entropic Map, a GPU-efficient approximation of the optimal transport map on manifolds. Our experiments show that by respecting the intrinsic geometry of the data, RWEFM can generate whole single-cell samples in hyperspherical latent spaces and protein conformational ensembles on the torus. Code and tutorials are available at \href{https://github.com/AnonRWEFM/RWEFM}{RWEFM}.

Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant algorithmic approach relies on the Jordan--Kinderlehrer--Otto (JKO) scheme. JKO-based methods are inflexible to time discretisation and require solving costly optimal transport problems. We take a residual approach, enforcing that the continuity equation conditions are satisfied via a non-negative loss function, whose minimum is the WGF. Combined with a data-fitting divergence, this gives a single global objective. This perspective unifies several existing methods, and leads us to discover a new particle-based method, \emph{stitching}, that is simulation-free and robust to large gaps in observation times of the dynamics. We demonstrate that the stitching method achieves state-of-the-art performance across trajectory inference benchmarks.

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.

Flow matching learns continuous-time transports from a simple source distribution to a target data distribution by training a velocity field on intermediate states along interpolating trajectories. However, because the model observes only the projected data-space state $(x_t,t)$, different transport trajectories can induce conflicting velocity directions at nearby intermediate states, leading to curved transport paths that limit the fidelity of low-NFE sampling. To address this limitation, we propose \emph{State Augmented Flows} (SAF), a lightweight framework that lifts flow matching into a transient augmented state space. SAF transports an augmented state $(x_t,z_t)$, where auxiliary coordinates provide additional contextual information during transport while vanishing at the terminal time. This enlarges the state observed by the velocity model without changing the final sample space, and is compatible with existing coupling strategies and flow-matching architectures. Across MNIST, CIFAR-10, and ImageNet-32, SAF consistently improves over the rectified-flow baseline, with the largest gains in the low-NFE regime. These results suggest that augmenting the transported state provides a new and complementary mechanism for improving flow-based generative modeling.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on $(\mathbb S^{d-1})^L$ both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

The Maximal Independent Set (MIS), Dominating Set (DS), and Vertex Cover (VC) problems are fundamental combinatorial optimization problems with wide-ranging applications. We identify a key property of these problems: by finding a cut in the graph and determining the states of vertices associated with the cut, the graph can be decomposed into multiple subgraphs whose solutions are independent of each other. Therefore, we classify MIS, DS, and VC as Edge-Cut Separable Problems (ECSPs). This property enables a natural divide-and-conquer strategy, which significantly reduces the computational complexity and allows neural networks to scale to large-scale graphs that were previously intractable. Based on this property, we propose a recursive framework that leverages this property to approximately solve ECSPs, namely \ours. Our framework consists of two major components: a partitioner that identifies a cut in the graph, and a predictor that solves the cut-determination sub-problem (CDSP) to determine the states of vertices associated with the cut. By recursively applying these components, RGF generates a complete solution for the original ECSP instance. Additionally, through partial prediction, the memory consumption is significantly reduced, enabling RGF to handle real-world large graphs. Experimental results validate the advantages of RGF: the performance of our method is up to 2.13\% better than the state-of-the-art machine learning (ML)-based approach, and our approach can handle real-world large graphs with up to 11M vertices.

Generative models can produce images nearly indistinguishable from real data, yet rigorous and interpretable evaluation remains challenging. Conventional metrics such as FID provide only scalar scores with limited diagnostic insight. Widely adopted CLIP-based metrics enable semantic evaluation beyond simple training class labels, but inherit limitations from CLIP’s training paradigm that restrict attribute-wise analysis. We propose RA-CLIPScore, a novel metric that mitigates these issues and extends CLIP-based evaluation to spatial distribution alignment, measuring whether generated objects adhere to the positional priors found in the training data. RA-CLIPScore introduces dual prompts to decouple competing attributes and leverages local patch tokens to capture fine-grained regional semantics. We evaluate image generative models on their ability to match both attribute and spatial distributions of the training data. Extensive experiments show that RA-CLIPScore provides more robust and interpretable evaluations than prior methods, particularly under distribution misalignment or partially irrelevant textual attributes. We further demonstrate how it reveals previously undocumented regional tendencies in generative models.

Ante-hoc interpretability methods based on prototypes provide highly accurate explanations by utilizing the intuitive "this looks like that" reasoning paradigm. On the other hand, post-hoc models can explain predictions for a single image without relying on an underlying dataset or requiring costly neural network retraining. Recent approaches successfully solve the retraining problem for prototype-based networks. However, they still face a fundamental limitation: they require access to a subset of data (e.g., a test or validation set) to search for and extract the visual prototypes. In this paper, we address this issue and introduce ProDG: Data-Free Generative Prototypes for Post-Hoc Explainability, a novel framework that leverages generative models to synthesize pure, high-fidelity prototypes directly from the frozen model's weights, completely eliminating the dependency on any external data. By establishing this new frontier in Data-Free XAI, DGP unlocks robust visual interpretability for privacy-sensitive domains, where original data is strictly restricted or fundamentally inaccessible.

Generative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations. In these settings, a method can achieve strong pointwise accuracy while still failing to capture the true posterior through mode collapse, over-confident uncertainty, or averaging incompatible solutions. We introduce PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers. PosteriorBench evaluates four physics-based inverse problems: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. For each task, we construct high-fidelity reference posteriors using slow but established procedures such as rejection sampling and Markov chain Monte Carlo, enabling direct assessment of whether solvers recover the full set of solutions rather than the single best sample. The benchmark spans sparse sensing, low-resolution observations, nonlinear forward models, varying noise levels, and multimodal priors, with a unified pipeline for distribution matching, uncertainty quantification, and hyperparameter calibration. Our experiments reveal substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness and that guidance weights and generation noise are key to posterior-variance calibration.

Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be path-independent. Path independence is crucial because it ensures that transformations depend only on the initial and target distributions, not on the specific path. In this work, we introduce \textit{Path-independent Flow Matching (PiFM)}, a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that PiFM generalizes Flow Matching to higher-dimensional parameter domains while enforcing structural conditions that ensure consistency of composed transformations. In addition, we show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter, linking the framework to a notion of distributional interpolation. To enable practical training, we propose a tractable, simulation-free objective that regresses onto multi-parameter conditional probability paths. We showcase empirically that PiFM outperforms other approaches on both synthetic and real world data in interpolating path-independent trajectories and generating desired out of distribution samples. Our code is available at \url{https://anonymous.4open.science/r/Pi_flow_matching-C83F/}.

Preference ranking modeling is important for selecting and adapting language-model responses to human preferences. Compared with deterministic ranking methods, generative preference ranking models the prompt-response data distribution, providing richer uncertainty characterization and sample diversity for learning a more expressive ranking boundary. Recent work improves modeling efficiency by shifting generative preference ranking from textual space to embedding space, but without explicit preference-conditioned separation, the learned embedding distribution may still entangle preferred and rejected responses, producing ambiguous synthetic samples that weaken the ranking boundary. To address this issue, we propose PRISM, a Preference Ranking framework through dISentangled embedding Modeling. PRISM formulates embedding-level generative preference ranking with a unified class-conditional ELBO and decomposes this optimization objective to expose the encoded latent entanglement between preferred and rejected embeddings. This derivation motivates two practical preference-aware generation variants: PRISMMI, involving a deep class-separation objective, and PRISMMMD, catering a probabilistic aggregate-matching objective. Both variants learn a preference-disentangled embedding data distribution and synthesize data pairs that preserve ranking semantics for the generative ranking boundary. Experiments show that PRISM improves preference ranking performance and produces useful generated embeddings for downstream response selection. The anonymous code repository is available at:https://anonymous.4open.science/r/PRISM-915C/README.md.

We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure $P_0$ to a target measure $P_1$ by integrating a velocity field of the form $v_t(x) = \mathbb{E}[\dot X_t \mid X_t = x]$, where $X_{\bullet} = (X_{t}) _{t}$ is a stochastic process satisfying $(X _{0}, X _{1}) \sim {P _{0}} \otimes {P _{1}} $ and $\dot X _{t}$ is its time derivative. We investigate when $X _{\bullet}$ induces a _straight-line flow_: a flow whose pointwise acceleration vanishes and is therefore exactly integrable by any first-order method. First, we develop multiple characterizations of straight-line flows in terms of PDEs involving the conditional statistics of the process. Then, we prove that straight-line flows under endpoint independence exhibit a sharp dichotomy. On the one hand, we construct explicit, computable straight-line processes for arbitrary Gaussian endpoints. On the other hand, we show that straight-line processes do not exist for targets with sufficiently well-separated modes. We demonstrate this obstruction through a sequence of increasingly general impossibility theorems that uncover a fundamental relationship between the sample-path behavior of a process with independent endpoints and the space-time geometry of this process' flow map. Taken together, these results provide a structural theory of when straight-line generative flows can, and cannot, exist.

Diffusion-based models decompose sampling into many small Gaussian denoising steps—an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong few-step baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Generative models such as Diffusion Models and Flow Matching have improved multimodal trajectory planning in autonomous driving, but still suffer from inference latency and the lack of tractable probability densities, relying on heuristic trajectory selection. We propose BiDrive, a real-time end-to-end planning framework based on Normalizing Flows (NFs). By leveraging invertibility and exact likelihood estimation, BiDrive directly evaluates trajectory probabilities in a single forward pass, enabling principled maximum-likelihood-based decision making. To address the autoregressive bottleneck of expressive flows, we further develop a bidirectional distillation framework that compresses an autoregressive flow into a one-pass generator, achieving real-time inference (50 FPS) while preserving modeling capacity. The autoregressive model is used only during training as a probabilistic teacher. In addition, we introduce a latent-space optimization mechanism that incorporates differentiable safety and dynamic constraints for efficient test-time trajectory refinement. Experiments on NAVSIM closed-loop benchmarks demonstrate state-of-the-art performance in both safety and efficiency, highlighting the potential of Normalizing Flows for real-time trajectory planning. Code is available at: https://anonymous.4open.science/r/BiDrive.

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

We propose the Monge Inception Distance (MIND), a metric for evaluating generative models that addresses key limitations of the widely adopted Fréchet Inception Distance (FID). The MIND metric leverages the sliced Wasserstein distance to compare distributions by averaging one-dimensional optimal transport distances, efficiently computed via sorting. This approach circumvents the estimation of high-dimensional means and covariance matrices, which underlie FID's poor sample complexity and vulnerability to adversarial attacks. We empirically demonstrate three primary advantages: (i) it is more sample-efficient by one order of magnitude, (ii) it is faster to compute by two orders of magnitude, (iii) it is more robust to adversarial attacks such as moment-matching. We show that MIND with 5k samples can replace the evaluation performance of FID with 50k samples, providing high correlation with this standard benchmark and superior discriminative performance. We further demonstrate that even smaller sample sizes (e.g., 1k or 2k) remain highly informative for rapid model iteration.

Fine-grained image retrieval (FGIR) typically relies on supervision from seen categories to learn discriminative embeddings for retrieving unseen categories. However, such supervision often biases retrieval models toward the semantics of seen categories rather than the underlying appearance characteristics that generalize across categories, thereby limiting retrieval performance on unseen categories. To tackle this, we propose GAPan, a Generative Appearance Prior alignment network that reformulates the learning objective from category prediction toward appearance modeling. Technically, GAPan treats retrieval features with an invertible density model based on normalizing flows. In the forward direction, the flow maps all instance features into a latent density space, where each seen category is modeled by a class-conditional Gaussian prior and optimized via exact likelihood estimation. This formulation preserves richer appearance details by leveraging the invertible property of the flows. In the reverse direction, samples from the high-density regions of these learned priors are mapped back to the feature space to produce appearance-aware anchors that reflect intra-category variation. These anchors supervise a prior-driven alignment objective that aligns retrieval embeddings with category-specific appearance distributions, thereby improving generalization to unseen categories. Evaluations demonstrate that our GAPan achieves state-of-the-art performance on both widely-used fine- and coarse-grained benchmarks.

The commercialization of LLM applications is the next frontier in online advertising, with *LLM-native advertising* emerging as a promising paradigm by integrating ads into LLM-generated content. However, classic mechanisms are no longer applicable in this setting where the auction object is shifted from discrete ad slots to distributions over LLM outputs, and existing methods are impractical in industrial scenarios due to ignored externalities or high inference costs. To address these issues, we propose LLM-Auction, the *first* learning-based generative auction mechanism that *integrates* auction and generation. By formulating the allocation as preference alignment between LLM outputs and a mechanism objective that balances advertiser value and user experience, we optimize the LLMs to inherently model allocation externalities without extra inference cost. Theoretically, we identify the allocation monotonicity and continuity of LLM-Auction, and prove that a simple first-price payment rule exhibits favorable incentive properties. Furthermore, we build an LLM-as-a-judge simulation environment for quantitative evaluation, and experiments demonstrate that LLM-Auction achieves the state-of-the-art allocation efficiency while satisfying key mechanism properties.

Target trial emulation (TTE) provides a framework for answering causal questions using observational data when randomized controlled trials (RCTs) are infeasible. However, standard methods for treatment effect estimation have been developed in isolation, failing to jointly address the compounding challenges inherent to analyses of observational data such as electronic health records (EHRs). In particular, these challenges include time-varying confounding and missing-not-at-random (MNAR) missingness reaching 50\%-80\% for critical biomarkers. To address this gap, we propose a two-stage pipeline that jointly handles MNAR missingness and causal structure across time. CausalFlow-T, a Directed Acyclic Graph (DAG)-constrained normalizing flow with Long Short-Term Memory (LSTM)-encoded patient history, performs exact invertible counterfactual inference, eliminating the approximation errors and confounding biases where existing variational and adversarial methods fail silently. Ablations on four synthetic and one semi-synthetic dataset with known counterfactuals confirm that its two core design choices address strictly non-overlapping failure modes (DAG constraints for confounding separation, exact inference for structural propagation) with neither compensating for the absence of the other. To handle the incomplete data CausalFlow-T receives as input, we propose an LLM-driven evolutionary imputer and evaluate it with three LLM backends, including two open-source models. Across 30\%-80\% MNAR missingness, the imputer achieves the best pooled rank across biomarker and causal metrics, leading on point-wise accuracy and temporal extrapolation while maintaining average treatment effect (ATE) recovery where statistical methods progressively degrade. Applied to a cohort of adults with type 2 diabetes in Swiss primary care initiating a GLP-1 receptor agonist or SGLT-2 inhibitor, the pipeline recovers a per-protocol weight-loss difference of $-0.98$ kg [$95\%$ CI $-1.01$, $-0.96$] favoring GLP-1 receptor agonists, consistent with RCT evidence and estimated directly from realistically incomplete real-world EHR data.