生成模型理论与方法

Heterogeneous federated learning requires clients with diverse computational capacities to collaboratively train a global model, where each client trains a capacity-constrained submodel. Existing methods select submodel parameters using heuristic importance measures---most prominently parameter magnitude---without theoretical justification for why these measures support convergence. We identify a fundamental gap: existing parameter selection criteria lack theoretical grounding in the convergence framework, partial client participation introduces additional estimation effects in the Fisher scores. We propose FedFIbOS: Fisher Importance-based Optimal Submodelling for heterogeneous federated learning, using Fisher Information in a principled criterion derived from minimizing submodel masking error. %We formally establish when magnitude selection is equivalent to Fisher selection fail under non-IID heterogeneous federated learning. We theoretically formulate submodel selection through a Fisher-weighted quadratic masking surrogate and show that the raw Fisher top-$k$ rule implemented by FedFIbOS solves this surrogate under a Fisher-dominant ranking condition. The resulting method retains the convergence structure of the underlying masked federated optimization bound. Fisher scores are efficiently estimated from empirical diagonal Fisher information using squared gradients, enabling stable and adaptive parameter selection without additional optimization overhead. Experiments on CIFAR-10, CIFAR-100, and AGNews under pathological and Dirichlet non-IID settings show FedFIbOS achieves ${\approx}10%$ higher accuracy than the state of the art, with improvements becoming more pronounced under stronger heterogeneity.

Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.

Few-step distillation reduces the inference cost of image-to-video generation, but directly reusing LoRA adapters trained for long denoising trajectories can weaken their intended effects and degrade video quality. We observe that adapters with similar measured static parameter geometry can behave differently under the shortened target schedule, motivating response-aware transfer. We propose DART, a training-free reparameterization method that transports source LoRAs into aligned coordinates through a low-rank distillation bridge. Paired forward evaluations measure channel-level incremental responses under the target schedule to fit coefficients that calibrate response direction, source-relative magnitude, and timestep allocation. Coordinate transport establishes update directions, while calibration adapts their contributions, requiring neither source training videos nor backpropagation. Experiments across multiple distilled I2V models demonstrate improved generation quality and aggregate functional retention over direct reuse. Further analyses show that coordinate transport complements response calibration, with adapter-level benefits encompassing both functional preservation and reduced negative transfer.

Characterizing the physical properties of clay and cementitious materials matters across many fields, from materials science to geological waste disposal. Property simulation typically calls for 3D imaging, which is expensive, not always accessible, and technically limited for certain materials. Recent progress in deep generative models offers a way around this, reconstructing 3D volumes from the more easily acquired 2D images. Among GAN-based methods for 3D microstructure generation, SliceGAN has shown strong results for homogeneous isotropic and anisotropic systems. It struggles, however, to capture the finer detail of more complex heterogeneous microstructures, which motivates alternative generative frameworks. We introduce a hybrid approach that draws on the stability and generation quality of denoising diffusion models. Since no 3D ground truth is available, we replace the standard denoising loss with an adversarial loss, which yields a stable training process in our experiments. We show that the resulting model generates microstructures of varying complexity with minimal slice artefacts and close agreement with ground-truth phase fractions and structural descriptors.

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.

Autoregressive language models (ARMs) are constrained by sequential, left-to-right generation, while masked diffusion models (MDMs) enable parallel decoding but suffer from high computational overhead due to the inability to reuse Key-Value (KV) cache and from incoherent generation arising from learning dependencies over an intractable space of token combinations. We introduce Zarya, a family of hybrid language models that jointly optimizes an autoregressive (AR) objective and a masked-diffusion objective within a single architecture. Zarya structures training data into variable-size slots and employs a curriculum that gradually increases slot granularity, enabling a smooth transition from fine-grained AR learning to coarse-grained diffusion learning. At inference, Zarya provides two distinct decoding paradigms through a unified interface: (i) MDM sampling with first-hitting denoising, and (ii) slotted speculative decoding that interleaves inter-slot diffusion-based selection with intra-slot autoregressive infilling, achieving full KV cache reuse. The training and inference regimes are fully decoupled, allowing a model trained with any configuration to be deployed in either mode. Extensive configurability --- including grouped noise patterns (Prefix Completion, Fill-In-the-Prefix, Fill-In-the-Middle), ordered sampling schedules, and noise-level permutation strategies --- enables flexible research exploration. We release Zarya models publicly in sizes 0.6B, 1.7B, and 4B, demonstrating performance on standard benchmarks while offering a principled integration of autoregressive and diffusion paradigms.

A popular selling point of diffusion large language models (dLLMs) is their capacity for parallelism: the ability to generate sequences of text far more efficiently than autoregressive models, which require one forward pass per token. Yet among the many competing paradigms for dLLMs, from masked to uniform to Gaussian diffusion, principled understanding of how these different proposals compare in parallelism remains limited. In this work, we initiate a fine-grained comparison of the capacity for parallelism among these three leading approaches and prove the following: - Uniform and Gaussian diffusion can sample in a number of forward passes which scales with the dual total correlation of the underlying distribution, a measure of intrinsic complexity which can be much smaller than the context length. Previously, it was only known how to achieve this using masked diffusion. - For a certain family of random empirical measures, we show that $\widetildeΘ(\sqrt{d})$ forward passes are necessary and sufficient to sample using uniform or Gaussian diffusion, yet there exist approximate score oracles for which $\widetildeΩ(d)$ forward passes are needed for masked diffusion. This establishes the first provable separation in parallelism between the three prevailing dLLM paradigms. Contrary to popular intuition that masked diffusions are harder to parallelize because they must commit to token values, the latter separation instead comes from the fact that the critical windows in masked diffusion sampling are asymptotically narrower than those in uniform and Gaussian diffusion sampling.

Retrieval-Augmented Generation (RAG) introduces a specific failure mode in discrete diffusion language models: when retrieved context contradicts parametric knowledge, the iterative denoising process becomes a visible battleground between competing knowledge sources. We identify temporal semantic divergence as an observable for detecting these conflicts and introduce the Trajectory Variance Score (TVS), a simple and interpretable measure of this divergence. TVS computes the mean pairwise cosine distance of answer embeddings across independent stochastic denoising trajectories, capturing the temporal tug of war between parametric and contextual attractors. Requiring as few as two parallel inference runs, TVS is computationally lightweight. Across four diverse datasets (Synthetic, SciQ, PopQA, and CounterFact), a simple Logistic Regression classifier using TVS achieves $70.10%$ accuracy and $0.7647$ AUROC on LLaDA. On Dream 7B, increasing the number of trajectories from two to five improves accuracy from $63.91%$ to $69.62%$. More complex sequential models provide only marginal improvements over the linear classifier. Evaluation across LLaDA and Dream 7B demonstrates that conflict-induced trajectory dynamics and their key properties transfer across distinct diffusion architectures.

We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.

Generative models are increasingly central to many de novo discovery pipelines, in which designs are generated at scale and filtered through virtual screens to determine a set of candidates to experimentally validate. While Bayesian optimization (BO) is a natural fit for this setting, as it uses past evaluations to guide future proposals, the computational overhead required for its sequential decision-making becomes a bottleneck when virtual screens are relatively cheap. We make BO practical in this regime by exploiting the unique combination of a linear model constrained to a spherical domain where high-dimensional latents concentrate. We build off recent work justifying the use of linear surrogates, while deriving nearly closed-form solutions to the surrogate modelling and acquisition problems that exploit spherical symmetry. The result is at least a 100x speedup over state-of-the art baselines, with matching or improved performance across molecular and image generation benchmarks. Altogether, our method makes BO a practical drop-in for de novo pipelines where it was previously too slow to consider.

In this paper, we introduce layer-wise curriculum learning for efficient LLM compression. The proposed method facilitates the knowledge transfer from the teacher model to the student model, utilizing a curriculum learning approach that begins with easier optimization tasks and progressively tackles harder ones. In order to adopt the layer-wise learning in LLM compression, we partition the whole model into multiple segments consisting of layers, thereby enabling more computationally efficient knowledge transfer for LLMs. Based on our theoretical analysis of cumulative error phenomenon, layer-wise curriculum learning accelerates convergence while stabilizing the knowledge transfer process. In addition, we present a feature caching method with a multi-threading strategy to efficiently address feature misalignment across layers, maximizing GPU utilization. Consequently, our method exhibits advanced model compression performance, as well as high computational efficiency in terms of minimized memory usage and short training hours. Experiments on multiple datasets show that the proposed method achieves state-of-the-art performance while reducing GPU memory usage and training hours by more than 50% on BERT and GPT-2. Moreover, it outperforms the other pruning methods on LLaMA-family and Qwen models under the same training hours, with a lower GPU memory footprint.

Text-to-image generative models are widely used in professional and creative settings, yet how they represent gender across occupations — and whether newer models are fairer — remains poorly understood across multiple generations. We evaluate gender representation across 20 occupations, 5 prompt templates, and 4 Stable Diffusion model generations (SD 1.5, SD 2.1, SDXL, SD 3 Medium), generating 8,000 images with n = 100 per occupation-model cell (5 prompts x 20 images), and classifying all with DeepFace. Across the 8,000 open-source images, 76.4% show male subjects (95% CI [75.1%, 78.7%], p < 2.2 x 10^-16, Benjamini-Hochberg adjusted). More strikingly, 57.6% of images for historically female-coded occupations show male subjects (raw p = 3.43 x 10^-22, BH-adjusted p = 1.71 x 10^-21). All nine significant tests reported in this paper survive BH correction across 10 tests. When compared against U.S. Bureau of Labor Statistics workforce data, models underrepresent women by 20-46pp on average, with particularly large deviations for near gender-balanced occupations: scientist (48% female in BLS, 82-99% male in model outputs) and cleaner (46% female in BLS, 80-92% male in outputs). Model generations do not improve steadily: bias worsens from SD 1.5 to SDXL before partially recovering in SD 3 Medium. A preliminary comparison with GPT-image-1 on five occupations suggests lower bias than open-source models, though the practical effect is small (Cramer's V = 0.080) and the comparison is exploratory. No model achieves gender parity.

The traditional Batak Ulos weaving industry faces growing challenges in producing diverse, innovative motifs due to limitations in conventional, manually driven design methods. This study proposes a multimodal generative framework integrating a fine-tuned Latent Diffusion Model (Stable Diffusion XL v1.0 via LoRA) with a Multimodal Large Language Model (LLaMA 1.5-7B) to enable controllable, culturally faithful Ulos motif generation. Four complementary conditioning mechanisms: text, image, representation, and semantic map (via ControlNet) jointly guide the generation process, each governing a distinct aspect from semantic intent to spatial layout. A five level ablation study across three scenarios (shape transformation, colour variation, and high-complexity input) shows that conditioning effectiveness is not proportional to the number of mechanisms combined: Text + Image + Semantic Map achieved the best FID (270) and CLIP Score (0.65 - 0.70) but the weakest SSIM (0.65), while Text + Image + Representation offered the best overall balance, with stable SSIM (0.84) and competitive FID (280). Combining all four mechanisms yielded the weakest FID (330), indicating conflicting optimization signals. Qualitative evaluation by nine weavers and thirty public participants confirmed statistically significant positive acceptance (Wilcoxon, p=0.007 and p<0.001, respectively). A web-based prototype supporting text-to-image and image-to-image generation was also developed, offering a practical digital design tool for cultural heritage preservation.

Structured prediction is the simultaneous prediction of multiple labels, and is widely used in various fields, such as natural language processing and computer vision. In this paper, we study binary node label recovery on signed graphs with edge-flip noise, a model introduced by (Globerson et al., 2015), via a simple spectral method that decodes node labels from the signs of the principal eigenvector of the noisy signed adjacency matrix. We develop graph structure-agnostic theoretical guarantees for approximate inference of node labels as well as guarantees for maximum angle deviation with respect to the ground truth node labels. By leveraging tools from matrix concentration theory and eigenvector perturbation analysis, we derive new concentration inequalities that explicitly quantify the effect of the spectral gap of the adjacency matrix, number of nodes, degree distribution, and noise level. As a corollary, we relate our general results to the Cheeger constant and provide results for different classes of graphs. We perform several synthetic experiments to validate our theory. To the best of our knowledge, we are the first to provide theoretical guarantees for the spectral-based approach. As a byproduct of our analysis, we derive technical results that might be of independent interest and useful for other machine learning problems.

Diffusion and flow-matching models are typically trained by corrupting data through independently sampled Gaussian noise. While simple and scalable, this forward process induces arbitrary data-noise couplings, forcing the network to learn high-curvature transports between unrelated endpoints. Existing optimal-transport methods reduce this burden by reassigning fixed noise samples to data, but the source noise distribution itself remains passive. To address this, we introduce Contrastive Noise Alignment (CNA), a training-time method that creates dynamic, contrastive couplings by optimizing the noise representations directly. By modeling the noise batch as an interacting particle system, CNA employs a cross-modal InfoNCE objective to align noise particles with their paired data targets. To prevent spatial collapse, this alignment is regularized using an angular entropy term and a radial norm penalty. We show theoretically that this equilibrium asymptotically preserves Gaussian structures, maintaining tractability during inference. Empirically, CNA improves the alignment between noise and data, reduces flow curvature, and provides better generation quality with fewer required sampling steps. For few-step, pixel-space generation (2-4 NFEs), CNA reduces FID by over 50% compared to standard rectified flow, and by at least 24% against Optimal Transport baselines.

We establish convergence bounds for deep $V$-learning with horizon $H$. The algorithm fits a scalar value function to targets from executed transitions and selects actions using a predictive model and the value function. For current observed-successor targets with fresh true-kernel outcomes, the conditional mean is $\mathcal{T}^βV$, which averages over behavior-policy actions. The Bellman optimality update is $\mathcal{T} V$. We decompose the update error into six residuals: fitting, transition reuse, target construction, replay, action selection, and exploration. Under $L^s$ concentrability, their $L^p$ norms ($p=s/(s-1)$) control expected $L^1$ policy loss. The bound explicitly weights residuals from only the last $H-1$ update blocks, plus an initialization term for shorter runs. We quantify the cost of a shared sampling distribution across horizon levels. For statistical error bounds of order $n^{-ν}$, we derive optimal continuous allocations and an integer allocation whose objective is within a factor $2^ν$ of the constrained optimum. A margin condition with exponent $α$ gives action error of order $Λ^{1+α/p}$, where $Λ$ combines network drift and score error; a one-step construction proves the exponent sharp. Bounds on the distance between frozen and optimal scores transfer an optimal-gap condition to frozen-iterate gap bounds while retaining the mass of optimal ties. Survival probabilities and coverage conditions at deployment yield bounds for policies selected with approximate scores. Separate spatial ReLU networks per horizon level give a conditional neural regression rate, and the finite-state case gives a log-free expected fit rate. These results give expected policy-loss consistency for the fixed-horizon generative-reset approximate-ERM procedure with exact action scores and provide an explicit residual-decay criterion for FIFO/interleaved SGD.

We study the convergence of Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known up to a normalisation constant. By combining Wasserstein transport with Fisher-Rao birth-death dynamics, WFR flows balance exploration and selection. These flows have been recognised as a promising mechanism to accelerate convergence beyond Langevin dynamics. We show that for a class of strongly log-concave target distributions satisfying additional curvature conditions, WFR flows preserve strong log-concavity, in contrast to Wasserstein flows which enjoy this property only in the Gaussian setting. Exploiting this result, we derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, without requiring a warm-start as required in current estimates. In particular, we show that the convergence rate decomposes additively into Wasserstein and Fisher-Rao contributions, thereby confirming a recent conjecture within this setting. These results provide refined convergence guarantees and further develop the theoretical foundations of WFR gradient flows for sampling and Bayesian inference.

Recent Omni-Modal Generative Models (Omni-Models) have advanced content generation toward unified modeling of text, images, video, and audio. MiniMax-H3 exemplifies this transition by combining multimodal context understanding with joint audio-visual generation in a shared latent framework. Its unified architecture raises a fundamental question: Can multimodal alignment improve the model's world reasoning, and what new evaluation paradigms do omni-modal inputs enable? To investigate this question, this work introduces a comprehensive evaluation framework organized around four complementary dimensions of physical world reasoning. Unlike existing evaluation frameworks for video generation and world models, which are often constrained by limited input modalities and evaluation settings where prompts closely match the target video content, our evaluation is specifically designed to exploit the multimodal inputs of Omni-Model. We construct a diverse set of novel tasks that require models to integrate complementary information across modalities. Specifically, we consider four scenarios, including implicit prompts paired with multiple frames, audio-image, prefix-videos, and audio-video inputs. Every single modality provides only partial evidence about the underlying event, requiring the model to jointly reason over the complementary semantic cues to infer latent event states and future dynamics. Across 517 evaluation instances, MiniMax-H3 achieves an overall success rate of 41.97%. Video-based Decision Reasoning yields the highest success rate at 56.00%, while Audio-based Disambiguation Reasoning is the weakest, reaching only 27.40%. These results indicate that effective multimodal integration remains key to fully exploiting the benefits of diverse input modalities. The project is available at https://github.com/gulucaptain/MiniMax-H3-Reason.

Direct preference alignment methods are widely used to align large language models (LLMs) with human preferences because of their computational and memory efficiency. However, likelihood displacement motivates alternative ways to extract information from preference pairs with small likelihood margins. In this paper, we propose and analyze Comparison-based Preference Optimization (ComPO), a zeroth-order alignment method based on comparison oracles. ComPO extracts directional information from these pairs without directly optimizing a differentiable preference loss on them. We establish a convergence guarantee for its basic offline scheme under smoothness, gradient sparsity, and compatibility between the oracle and a latent objective. We further introduce online ComPO, which retains the offline comparison mechanism and uses unlabeled policy generations for reverse-KL control relative to a reference policy. Following the coverage perspective of preference fine-tuning, we establish a performance guarantee for a basic constrained scheme under local coverage and in-distribution pairwise reward accuracy. Experiments on Mistral, Llama, Gemma-2, Qwen3, and Gemma-3 models demonstrate improvements over existing direct alignment methods, including length-controlled win rates, with pair-level diagnostics providing evidence consistent with mitigating likelihood displacement.

This thesis develops robust and efficient AI frameworks for accelerating crystalline materials discovery by addressing both major stages of the materials-design pipeline: crystal property prediction and crystal structure generation. Motivated by the high computational cost of Density Functional Theory (DFT) and the limited availability of labeled materials data, the thesis explores graph representation learning, pretraining, multimodal learning, and generative modeling for scalable materials design. For property prediction, the thesis first introduces CrysXPP, which learns transferable crystal representations through unsupervised graph autoencoding, reducing dependence on large property-labeled datasets. It then proposes CrysGNN, a large-scale self-supervised graph pretraining framework that captures atomic connectivity, chemical attributes, and global structural information and transfers this knowledge to downstream property predictors through knowledge distillation. CrysMMNet further enriches crystal representations by jointly modeling graph structure and textual descriptions, thereby incorporating both local chemical and global structural knowledge. For crystal generation, the thesis introduces TGDMat, a text-guided joint diffusion framework that jointly models lattice parameters, atomic types, and atomic coordinates while incorporating textual structural knowledge during denoising. This enables the generation of more valid and stable periodic materials while also supporting conditional generation from natural-language descriptions. Overall, the thesis establishes a unified AI-based framework for data-efficient property prediction and controllable crystal generation, demonstrating how graph learning, multimodal representations, and generative models can reduce computational cost and improve the scalability of materials

Humans efficiently learn new tasks by reusing a rich repertoire of motor skills across different goals and contexts. A similar strategy can also be used to enable simulated characters to efficiently perform new tasks by leveraging reusable motor skills. To support a wide range of downstream tasks, the learned repertoire should be diverse, consisting of distinct behaviors as well as spatial and temporal variation within each behavior. A commonly used method for learning diverse skills is by maximizing the mutual information between skill latents and the states produced by a policy. The marginal state entropy promotes broad behavioral coverage, while the conditional entropy encourages consistent behaviors from each latent. However, directly estimating the marginal state entropy is intractable in high-dimensional control problems. Prior methods therefore rely on indirect latent-space approximations or coarse estimators of the state distribution. These approximations may not effectively promote broad coverage of the state space, resulting in skills with limited behavioral diversity and reduced utility for downstream tasks. In this work, we propose Diffusion Skill Discovery (DSD), a skill discovery method that uses a diffusion model to approximate the entropy gradient of the policy-induced state distribution through score matching. The resulting objective encourages the discovery of skills that produce a broader range of behaviors for high-dimensional humanoid control. The learned skills are reused in two downstream control settings: hierarchical control with a task-specific high-level policy and zero-shot control through latent selection from offline trajectories. Our experiments show that DSD discovers a broader repertoire of reusable motor skills than prior skill discovery methods, leading to the emergence of complex and agile behaviors that can be reused across downstream tasks.

Diffusion models are increasingly used to generate synthetic training data, but precise label control remains difficult when the conditioning signal is low-dimensional and coarse. Text-conditioned images are judged by broad prompt consistency, whereas supervised training requires precise correspondence between each image and its numerical label. This is challenging in eye tracking, where a 4D binocular gaze is expressed through subtle, spatially localized pupil and iris geometry. We introduce GazeDiT, a diffusion model that generates images for a requested 4D gaze through an internally constructed spatial condition that grounds the global gaze label in this local geometry. During training, a frozen SegFormer extracts pupil/iris geometry from diverse real images, allowing the model to learn realistic appearance conditioned on that geometry. At inference, a physical eye renderer samples gaze-consistent geometries by varying anatomy and camera state, enabling diverse synthesis without a source image. GazeDiT achieves substantially lower tail gaze-label error than other diffusion baselines, approaching the error of the same frozen gaze estimator on real images. Its generated data also improves the downstream eye tracker, reducing gaze error on difficult cases from 3.05° to 2.80° in the smallest cohort.

Speculative sampling accelerates diffusion model generation by drafting inexpensive candidate states and correcting them under a coupling that preserves the target distribution exactly, reducing the number of expensive target evaluations. Existing diffusion samplers, notably those based on reflection maximal coupling, are topologically constrained: their lookahead drafts form a chain graph, a single linear sequence, which inherently limits the acceptance rate per target evaluation. We connect speculative sampling in diffusion models to relative entropy coding (REC). This perspective shows the lookahead need not be linear and motivates our central contribution, draft trees, which enrich the candidates considered per round and lower the target function evaluations. We further adopt greedy rejection sampling, an REC algorithm, as the draft-target coupling, improving acceptance while guaranteeing exact target samples. Experiments across diverse target and draft models demonstrate up to 8.3% acceleration over the reflection coupling baseline in practical settings.

Many proteins function through transitions between conformational states, yet rare states are rarely sampled by diffusion models trained on an equilibrium ensemble, demanding better sampling methods. We introduce METALICA, which implements Metadynamics on a pretrained diffusion model via Replica Exchange. It accumulates a bias potential along a Collective Variable, repels new samples from previous ones through biased sampling, and reweights samples onto the unbiased distribution. METALICA holds one replica per diffusion level, forming a Markov Chain that evolves through inter-replica communication and is refined in place as the bias grows. METALICA is the dual of sequential control, in which Sequential Monte Carlo parallelizes the sampler over a batch of particles. Parallelism over the levels of the diffusion-time schedule instead allows METALICA to generate samples from long chains, essential for the discovery of rare events, with accuracy set by run length rather than by the memory available. We validate on a bimodal target with known free energies, then apply METALICA to the unfolding of a protein. At a budget for which sequential control yields no unfolded structure, METALICA populates the basin and resolves a second free energy minimum.

Near-field to far-field transformation is central to large-aperture antenna testing, yet two coupled challenges remain: costly phase acquisition at millimeter-wave bands and violations of the centering assumption under offset mounting. Existing methods address these issues separately, requiring either dense full-field data or offset vectors. We tackle both jointly by exploiting a key observation: amplitude fields under different offsets are coordinate-transformed views of the same near field. The challenge is to recover the center-aligned field from offset amplitudes without a phase or offset vector. We propose AntennaFlow, a three-stage framework: a contrastively learned encoder that maps offset views to an offset-invariant embedding, a deterministic flow-matching transport that maps offset amplitudes to center-aligned ones, and the Simplified Extrapolation Technique, whose Green-function Taylor expansion is valid only for centered fields. Experiments show that AntennaFlow enables fast, phaseless, offset-vector-free NF--FF reconstruction from sparse amplitude-only measurements, consistently outperforming existing baselines while preserving physical consistency.

Text-to-image diffusion models often use a fixed number of denoising steps, balancing time costs and image quality. However, the optimal number of steps depends on the complexity of the input text prompt. We propose an adaptive diffusion controller that dynamically adjusts the number of steps to generate high-quality images efficiently, without additional model training. By leveraging a mixture of step schedules with varying step sizes and evaluating the error term discrepancy at each timestep, our method transitions between schedules to optimize performance. Experiments on COCO and DiffusionDB show that our approach reduces inference time while maintaining visual fidelity, offering a more efficient alternative for text-to-image diffusion models.

Cranial implant generation is an important task in medical imaging. Recent point cloud based generative methods, particularly flow matching, offer strong reconstruction quality and efficient sampling, but still require multiple neural function evaluations during inference. This limits rapid generation of multiple plausible implant candidates. We propose Teacher-guided Endpoint Distillation (TED), a simple one-step distillation framework for conditional cranial implant generation on point clouds. TED trains a one-step student using teacher-guided endpoint supervision and geometric matching losses, while avoiding explicit path straightening. We evaluate TED on the SkullFix and SkullBreak benchmarks. TED achieves the best overall performance on the SkullBreak dataset, remains competitive on SkullFix, and provides the strongest Chamfer distance performance among the compared one-step methods. In addition, TED generates implants in approximately 0.04s per sample. These results show that one-step distillation can substantially accelerate conditional point cloud implant generation without sacrificing reconstruction quality.

Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture this local heterogeneity. In this paper, we introduce a Voronoi-based partial optimal transport (VPOT) framework for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure. The key geometric idea is to localize the comparison of two mixing measures to extended Voronoi neighborhoods and use partial optimal transport to accommodate the unequal masses of their local restrictions. Within each neighborhood, the first-order POT discrepancy is raised to a power determined by the number of locally competing atoms, allowing the resulting loss to adapt to the local degree of singularity. Under suitable regularity and strong identifiability conditions, we establish uniform local and global upper bounds for a maximum likelihood estimator under the VPOT loss. These bounds reveal a configuration-dependent form of parameter estimation: less singular local configurations admit faster convergence, whereas the most singular configuration recovers the classical worst-case behavior characterized by Wasserstein-based analyses. We further establish a minimax lower bound showing that the convergence rate for estimating the mixing measure under the VPOT loss is optimal. Our results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components. Overall, VPOT provides a configuration-adaptive framework for capturing heterogeneous parameter-estimation behavior in finite mixture models.

Building accurate decision-support tools for next-generation air traffic control requires robust trajectory prediction models. We present a flow-matching architecture trained exclusively on historical aircraft trajectories, with no route labels or chart supervision. Trained on 1.15 million Automatic Dependent Surveillance-Broadcast trajectory windows collected over the San Francisco Bay Area, the model generates aircraft trajectory distributions that closely match historical traffic, reproducing known airspace structure around San Francisco Airport such as the shape of SFO's published NIITE FOUR departure procedure. Our model is trained directly on the native, irregular ADS-B sampling interval. Trajectory prediction is cast as sequence inpainting using a block-causal Transformer that denoises future state tokens conditioned on the observed history using Conditional Flow Matching or Denoising Diffusion Probabilistic Models. We compare our architecture against constant-velocity, deterministic-Long Short Term Memory, and Conditional Variational Autoencoders baselines. At matched parameter count, CFM outperforms DDPM by 11-26% in minADE@20, and both generative objectives surpass the CVAE baseline by 31-41%. We further show that the error degrades gracefully with prediction horizon, and the architecture remains effective when retrained on temporally decimated feeds. Lastly, we sample $K$ independent completions, yielding spatial probabilistic occupancy estimates that can serve as input to downstream conflict-risk estimation.

Exploring the chemical space of flexible molecules remains challenging because the vast number of possible compounds and conformations, together with the increasing cost and limited generalization of 3D generative models for larger and more complex molecules, restrict access to unexplored chemistry. Here, we introduce QALPA ("Quantum-Aware Learning for Property-space Augmentation"), a property-guided generative framework that combines an E(3)-equivariant diffusion model with active learning and efficient quantum-mechanical (QM) methods to iteratively explore targeted QM property manifolds. By coupling generation with physics-based evaluation, QALPA improves molecular sampling and model reliability in sparsely populated regions of chemical space. Our results show that training on complementary QM datasets spanning both small (QM7-X) and large (Aquamarine) drug-like compounds enables accurate molecular generation across a broad size range, improving transferability beyond the training distribution for complex property manifolds involving both extensive and intensive properties. As a proof of concept, QALPA coupled with the machine learning-augmented tight-binding method EquiDTB efficiently augments alloQM, a QM dataset introduced in this work, comprising 6,253 conformers of allosteric drug molecules, by populating sparse regions of the property landscape defined by the many-body dispersion energy and HOMO-LUMO energy gap. These results demonstrate that the integration of generative AI with efficient ML/QM methods offers a practical pathway toward augmenting sparse QM datasets and sustainably expanding the exploration of chemical space for molecular discovery.