Conditional Generative Modeling

Estimating conditional distributional potential outcomes (CDPOs) over time is important in medicine (e.g., to estimate patient-specific risks under different treatment sequences). However, this task is challenging because of time-varying confounding, yet existing adjustment strategies for this task are limited. In this paper, we aim to learn CDPOs under time-varying treatments using flexible generative models. Our contributions are two-fold. (1) We introduce a tailored adjustment strategy for our setting, namely, generative recursive g-computation. Our adjustment strategy recursively propagates full conditional outcome distributions rather than conditional means, modeling the variables of interest directly rather than full trajectories. Building on our adjustment strategy, we formulate simple generative learners for CDPO estimation. However, these learners can be sensitive to nuisance estimation errors, which motivates an orthogonal learner. (2) We thus introduce OrthoGen, a Neyman-orthogonal and doubly robust generative learner. Importantly, we show that OrthoGen further achieves rate double robustness and quasi-oracle efficiency under suitable conditions. Our learners are flexible and can be instantiated with different generative backbones (e.g., normalizing flows and diffusion models). Across experiments with synthetic, semi-synthetic and real-world datasets, we find that OrthoGen is highly effective. To the best of our knowledge, we are the first to propose a generative orthogonal learner for estimating CDPOs under time-varying treatments.

LiDAR point clouds of humans are extremely expensive to collect and annotate, thus represent a scarce resource that hinders the development of human analysis using this modality. To alleviate this scarcity, prior work relies on simulated human LiDAR, but such samples do not fully reflect the geometry and sensing characteristics of real observations. In contrast, we introduce HuLiGen, a generative model that generates human LiDAR point clouds from a parametric body model, using a point transformer trained with a flow-matching objective. We show that our generated point clouds are closer to the real capture distribution. Using HuLiGen to generate synthetic data, we propose a synthetic-only pretraining scheme for LiDAR-based HPE that achieves state-of-the-art performance, with even larger gains in low-annotation and low-data regimes, where MPJPE is reduced by up to 50%. Code, models and generated samples are available at https://github.com/valeoai/HuLiGen.

Diffusion models excel at image synthesis, but they remain limited in their ability to reliably satisfy structured spatial reasoning constraints. In conditional data distribution modeling tasks with implicit logical structure, such as puzzles defined by visible clues paired with consistent solutions, state-of-the-art generative models tend to approximate pixel-space distributions without learning the underlying logical rules required for inference. To address this limitation, we present a novel framework for spatial reasoning with diffusion models that leverages unsupervised object discovery and abstractions of object relations. We show that the relational knowledge derived from object-centric representations enriches diffusion models with structural primitives, allowing them to effectively guide the generative representation space during both training and inference, and enabling conditional image generation that satisfies reasoning constraints. Additionally, we introduce a large-scale generative spatial reasoning benchmark with four datasets inspired by human-solvable puzzles. Our results show that relational abstractions significantly improve reasoning capabilities of diffusion models on a variety of complex reasoning tasks, while enabling robust generalization in out-of-distribution settings.

Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learning. Realistic synthesis of patient-level clinical data requires jointly modeling heterogeneous static covariates, irregularly sampled longitudinal trajectories, and informative observation times - three tightly coupled components in practice yet rarely addressed together. We propose HyperNSDE, a continuous-time generative model that conditions a latent Neural SDE on static patient representations through a hypernetwork, allowing baseline characteristics to shape trajectory evolution beyond the initial condition without requiring a trajectory encoder, while stochastic latent dynamics capture realistic variability in generated paths. Observation times are modeled jointly through a latent-state-dependent intensity process, and training on irregular stochastic paths is stabilized via a deterministic-stochastic path decomposition with a non-adversarial signature-kernel objective. Experiments on simulated and real clinical datasets show improved observation-time fidelity and competitive performance, while matched-grid analyses reveal that forecasting and correlation metrics are affected by observation-grid regularity and trajectory smoothness.

Neurons of the brain exhibit a rich repertoire of electrophysiology dynamics with the same repeated stimulus eliciting very different voltage responses from the same cell. One common approach in biophysically detailed models is to capture this variability through ensembles of deterministic parametrizations, at a cost of hundreds of thousands of CPU hours. Existing machine learning surrogates inherit the same limitation, where a stimulus is mapped to a single voltage response. We address this challenge by learning a conditional generative model for single-neuron electrophysiology, using flow matching with a velocity field conditioned on the input current. On biophysically detailed models of two human cortical interneuron types, the generated responses closely reproduce the electrophysiological feature distributions, spike-time structure, and excitability profiles, even matching the experimental recordings from the corresponding human cortical neurons. Near the firing threshold, firing and non-firing responses coexist at the same stimulus amplitude, and at high amplitudes, ensembles may split into low- and high-firing modes near depolarization block. We show that our model recovers both modes in each case, while a neural operator baseline suppresses spiking near threshold and blurs the gap between modes at depolarization block.

Deep learning has revolutionised weather forecasting in recent years, especially through atmospheric foundation models, which offer competitive skill for a fraction of the computational costs of classic physics-based models. However, most existing foundation models are deterministic, limiting the generation of large ensembles for accurate uncertainty quantification, extreme weather risk assessment, and long-range weather forecasting. Furthermore, these models incur a large, often prohibitive, computational overhead to train from scratch. To address these shortcomings, we turn a pretrained deterministic prior model, namely the Aurora foundation model, into a generative ensemble-prediction model. To that end, we introduce a novel generative method, Denoising Stochastic Interpolants, combined with a replay buffer for Stochastic Differential Equation (SDE) rollout, enabling probabilistic training of SDE trajectories. Our stochastic foundation model, Xaurora, is finetuned from the small Aurora version, yet it approaches the state-of-the-art on global ensemble metrics and is competitive with the large version of Aurora. Our method is parameter and sample efficient, and generates skilful 15-day forecasts in 13 minutes. Our results demonstrate that deterministic foundation models can be efficiently extended into even stronger stochastic models.

Learning from trajectory demonstrations offers a route to active-inference control of complex systems whose dynamics are difficult to model explicitly. We introduce generative active-inference control (GenAIF), in which one generative trajectory model learns from demonstrations and measured action interventions to supply a goal-conditioned policy distribution and a state-to-observation likelihood mapping. From this control design, we derive three model requirements: (i) useful action proposals, (ii) accurate prediction under imposed actions, and (iii) probabilistic observation evidence for belief updating and expected information gain. We benchmark diffusion, autoregressive Transformers, conditional variational autoencoders (CVAEs), and flow matching in a MuJoCo manipulation task with multiple physical conditions. Diffusion delivers the strongest control across the tested dynamics, while CVAE combines comparable short-horizon prediction with much faster inference. Correct conditioning is decisive, and trajectory reuse offers further computational savings. In replay after an unannounced tilt change, pretrained diffusion updates belief fastest among the original models; fine-tuning on recovery demonstrations further accelerates identification and sustains accurate tracking. These findings support the use of shared generative trajectory models to connect action proposal, controlled prediction, and observation evidence within GenAIF.

Generative foundation models are attracting interest for their ability to produce desired outputs from demonstrations given at inference time, without updating parameters. However, since a few demonstrations cannot uniquely identify the intended task, the challenge is how to learn and sample from an output distribution that reflects this task uncertainty. In this work, we theoretically analyze how a Diffusion Transformer (DiT), pretrained across diverse tasks, learns and generates predictive distributions for a new query from demonstrations. We first show that the natural target to generate from finite demonstrations is not an output derived from estimating a single task, but rather a predictive distribution that captures the task uncertainty remaining after observing the demonstrations. We then prove that a DiT can learn this predictive distribution through score estimation, using attention to aggregate information from demonstrations and diffusion to generate samples. Owing to this property, with sufficient pretraining resources and diffusion sampling steps, the resulting DiT achieves the minimax optimal rate over a Hölder class of test-time tasks. These results imply that DiT acts as a statistically grounded in-context generator capable of generating distributions adapted to new tasks while retaining the uncertainty inherent in finite demonstrations.

We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.

Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual assignment mechanism. We develop a flow-matching approach that combines a sample-split, doubly robust training objective with a learned coupling between observed source outcomes and target outcomes drawn from a fitted conditional outcome model. To enable finite-step generation, we leverage a score-corrected stochastic sampler based on a Gaussian-smoothed interpolation. Our main theoretical contribution is a coupling-sensitive KL bound for constant-step Euler discretization: the error is controlled by moments of the source--target displacement under the chosen coupling, rather than by global uniform regularity of the velocity field, and has near-linear dependence on the ambient dimension. We also establish finite-sample non-parametric guarantees for the learned velocity and score fields when both the conditional outcome model and the source-target coupling are estimated from data. These bounds separate approximation, coupling-replacement, nuisance-estimation, generalization, and Monte Carlo errors and, combined with the sampler analysis, yield an end-to-end guarantee for counterfactual generation. Experiments on synthetic and semi-synthetic image benchmarks support the coupling-dependent theory and show that, at finite discretization budgets, the stochastic sampler can outperform the corresponding deterministic ODE sampler.

Weather reanalysis products rely on computationally intensive numerical weather predictions followed by data assimilation that corrects the forecast toward observations. Recent advances in deep generative models offer a cheaper alternative that shifts much of this cost from inference to offline training. However, existing generative approaches have been evaluated on synthetic observations or under different datasets and evaluation schemes, making it unclear which design choices improve real-world data assimilation. We present the first controlled benchmark of generative data assimilation for single-time near-surface analysis from real weather station observations. Using 11,849 NOAA MADIS stations across the contiguous United States and four near-surface variables, we hold the dataset, observation operator, and deep learning architecture fixed, and measure spatial generalization at held-out stations. The benchmark compares the major design choices proposed for generative data assimilation, including diffusion versus flow matching, pixel versus latent-space formulations, and multiple inference-time conditioning strategies, against a classical 3D-Var baseline. The benchmark reveals three conclusions. First, the best generative methods outperform 3D-Var (35.7% vs. 33.3% RMSE improvement over ERA5), although 3D-Var receives the ERA5 field at the analysis time as its background and the generative methods receive none. Second, full-gradient guidance consistently outperforms stop-gradient and initial-noise optimization. Third, other choices provide little measurable benefit: diffusion and flow matching perform nearly identically under matched conditions, and latent-space variable mixing does not help. Both advantages widen when stations are sparse. Together, these results identify which components of generative data assimilation improve spatial generalization in near-surface analysis.

We introduce Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. We present two designs. The first conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second factorizes the grand canonical distribution into a particle-number distribution and the corresponding canonical Boltzmann density. This factorized formulation can use any existing Boltzmann generator for the canonical component, encodes the known linear chemical-potential dependence analytically, and yields a tractable likelihood that supports self-normalized importance sampling (SNIS). Empirically, GCG accurately reproduces grand canonical observables on a Lennard--Jones fluid and methane adsorption in a zeolite, demonstrating generalization across chemical potentials and correction via SNIS and grand canonical Monte Carlo.

Mixture modeling is a long established machine learning technique for learning large sets of multi-modal data. While it is known that sequence-to-sequence models for dialog response generation suffer from the problem of low diversity, we hypothesize that it is because sequence-to-sequence models tend to learn a degenerate uni-modal distribution of responses. We then propose to incorporate a mixture of decoders into sequence-to-sequence models and try to make each decoder learn specialized topics in order to improve the diversity of generated responses. Our model is developed under the framework of conditional variational autoencoder (CVAE). We evaluate our approach on an open domain chat corpus and show improvement over strong baselines in quantitative measures and human evaluation.

Full detector simulation and reconstruction of collider events are projected to become major bottlenecks at the High-Luminosity Large Hadron Collider, motivating the development of fast, ML-based surrogates. At the same time, LLMs have driven fast progress in generative discrete modeling: autoregressive transformers trained on tokenized data now represent the state of the art across a range of generative tasks. We extend the discrete modeling paradigm by introducing a particle-level generative model trained on residual-quantized full-event data. We demonstrate the ability of this model family to perform conditional generation from detector-stable particles; we study its scaling behavior across a range of dataset and model sizes, characterize the effects of repeated data exposure and demonstrate that token-level loss systematically predicts downstream physical fidelity. These results provide an empirical framework for scalable collider full-event generation based on residual-quantized representations.

Crystal structure governs material properties, making crystal structure prediction (CSP) a fundamental problem in materials science. Generative models are a promising approach for solving this problem, but the prevalence of polymorphism, coupled with large unit cells and complex packing geometry, makes the molecular CSP task challenging for existing models. To address this, we introduce Coarse-Grained Open Materials Generation (CG-OMatG), an equivariant Riemannian flow-based generative model. CG-OMatG predicts molecular crystal structures \textit{via} a coarse-grained, hierarchical representation. CG-OMatG treats molecules as rigid bodies---performing both inter- and intra-molecular message passing to construct a geometric representation for molecular packings---and learns to reconstruct molecule centroid positions, orientations, and lattice parameters, conditioned on chemical species and conformer geometry. We train the model on subsets of the Open Molecular Crystals (OMC25) and Cambridge Structural Database (CSD) datasets. Further, we fine-tune the model \textit{via} policy gradient reinforcement learning to steer the model towards generating low-energy candidate structures. We validate the generated structures on the CSP blind test benchmark, assessing agreement with experimentally determined crystals using COMPACK packing-similarity analysis. CG-OMatG exhibits strong performance for generative molecular crystal structure prediction, paving the way for accelerated polymorph screening and organic solid-state materials discovery.

While modern language models demonstrate impressive generative capabilities, they often struggle with constrained, counter-intuitive creative tasks. To address this limitation, we explore chess puzzle generation as a rigorous testbed for computational creativity and reasoning, a domain where altering a single piece can invalidate an entire solution. We propose a novel approach for conditional generation of creative chess puzzles using masked diffusion models. Unlike previous methods, our non-directional diffusion approach allows for conditioning on specific tactical themes and partial board positions. We introduce a novel auxiliary task of simultaneous best-move prediction, which improves solution uniqueness by 11.6% and theme-conditioning accuracy by 2.5%. To further optimize solution uniqueness and theme conditioning, we establish a reinforcement learning framework adapted from Denoising Diffusion Policy Optimization (DDPO). This RL training increases the yield of unique and theme-matching positions by 89.1%. Finally, we release the first open-weights models (Appendix B) for chess puzzle generation, offering a new pathway for controllable, creative generation.

Tree-like branching structures are common in nature, from botanical trees to neurons, blood vessels and respiratory trees. Their branching shape often reflects function, making structural modelling central to understanding how these systems work. Because acquiring real-world 3D data is often expensive or infeasible, realistic generative models are valuable for simulation and data augmentation. Existing morphology-specific models either constrain how topology is generated or rely on hand-tuned, mechanistic procedures. Generic 3D graph generators, by contrast, do not exploit or enforce the structure of trees. We propose Autoregressive Frontier Expansion, a generative framework that constructs trees through an iterative expansion process, simulating the biological growth of real trees. At each step, a flow-matching model parameterised by an SO(2)-equivariant GNN expands the frontier by predicting whether each active branch bifurcates or terminates. We evaluate our method on cortical neurons and botanical trees in unconditional, class-conditioned, and morphology-guided generation. Across both domains, the generated morphologies agree closely with the reference distributions and, in conditional experiments, with the specified targets.

Cross-skeleton motion generation trains generative models to carry action structure and motion intention from one body to another. Yet a target motion that shows the right action has two explanations that the training data cannot tell apart: the model transferred the source clip, or it recovered a typical motion for the requested action. We show that this ambiguity is structural rather than incidental: under standard generative objectives, the source-conditioned retargeting map is non-identifiable in sparse heterogeneous motion domains. Unpaired distribution matching yields gauge non-identifiability: the latent spaces of different skeletons can be transformed relative to one another without changing the training evidence, so different source-conditioned maps fit it equally well. Sparse paired supervision admits the complementary failure mode, \emph{conditional-mean degeneration}: when clips are paired only by action, squared-error training converges to an average target motion that ignores the source clip. To make the missing evidence observable, we introduce Source-Instance Fidelity (SIF), a diagnostic that tests whether outputs differ from one another the way their source clips do, with the target skeleton and action held fixed. Under this diagnostic, methods that succeed at the standard action-level test on animal motion data often sit at the source-blind floor, while the methods that rise above it retain only a partial relational signal. Retargeting therefore needs objectives and evaluations that can identify the source-conditioned map it claims to learn. Project page: https://cross-skeleton-retargeting.netlify.app/.

Scalable Vector Graphics (SVG) are essential for modern industrial Computer-Aided Design (CAD). However, existing autoregressive SVG generation models are predominantly tailored for artistic creation and struggle to maintain the rigorous geometric fidelity and cross-view spatial alignment required for engineering drawings. To bridge this gap, we introduce \textbf{DrawingsDreamer}, a unified Large Language Model (LLM)-driven framework for multi-view vector-based engineering drawings generation. By formulating the generation of multi-view engineering drawings purely as a sequence modeling task, we eliminate the need of raster image encoders. We propose a Streamlined Representation utilizing hierarchical postfix tokenization, which guides the model to establish local geometric coordinates before assigning semantic boundaries. Optimized via a progressive task-aware curriculum schedule, \textbf{DrawingsDreamer} effectively transitions from localized structural repair to macroscopic generation in a unified model. Extensive experiments demonstrate that our unified model achieves strong performance in both geometric fidelity and syntactic accuracy across diverse conditional and unconditional generation tasks.

Large language models are increasingly used to simulate response distributions in social surveys. Prior work has achieved accurate population-level simulation for individual questions. Real questionnaires, however, ask each respondent a sequence of related questions. A simulated respondent should show coherent preferences across the whole questionnaire, not merely accurate distributions for isolated items. Existing single-item methods cannot accurately reproduce how the same person answers a complete survey. We propose FullRespondent-LLM (FR-LLM), which fine-tunes two specialized LLMs: a marginal model for each item's response distribution and a respondent-level autoregressive model for dependencies across answers. Marginal-Constrained Joint Projection (MCJP) then projects the autoregressive joint distribution onto the set satisfying the item-level marginals learned by the first model. This yields complete questionnaires with realistic cross-item relationships while retaining strong item-level accuracy. On two real-world social survey datasets, FR-LLM more accurately reproduces multi-question response patterns, maintains competitive single-item accuracy, and generalizes better to unseen populations and questions. In a small commercial-survey dataset, we use simulated responses to make pricing and stocking decisions; FR-LLM achieves the highest realized profit.

Generative models have found great success as data-driven methods of solving inverse problems. Two popular approaches work either by combining a pretrained generative prior with a known degradation model, or by training a conditional generative model directly from paired data. We target a setting that spans both regimes: unknown degradations can be learned from few paired examples, while known degradations can be learned from self-generated samples. We introduce Likelihood Score Approximation (LSA), a generative framework that keeps a pretrained unconditional model fixed and learns an observation-conditioned model that approximates the likelihood score from paired samples. Within a conditional stochastic-interpolant framework, LSA can be trained in either score or velocity coordinates, independently of the unconditional model's native parameterization, and supports both deterministic and stochastic sampling. We further show empirically that the prior model can be swapped post-training while keeping the same LSA model. Across speech and image inverse problems, LSA operates effectively even at roughly 0.01% of the full training dataset. On the ImageNet-256 benchmark it achieves competitive or better restoration quality than strong posterior-sampling baselines while requiring up to several orders of magnitude fewer network evaluations.

Critical mineral discovery is a positive-only problem: deposits are observed as sparse locations, while unlabeled regions are not reliable negatives, and similar geophysical signatures can arise from different subsurface states. We therefore model mineral targeting as learning a conditional spatial distribution over occurrence locations, $π(p\mid d)$, given geo-images $d$, rather than predicting a deterministic per-pixel score map. We introduce GeoCFM, a conditional flow-matching model that generates mineral occurrence point sets conditioned on multi-channel geo-images; GeoCFM learns a point-wise transport field in $\mathbb{R}^2$, using UNet features with point-conditioned velocity prediction to bridge dense rasters and sparse supervision without pseudo-negatives. On a synthetic magnetics--geochemistry benchmark with latent activation and on USGS Earth MRI data with a spatially disjoint tile split, GeoCFM improves geometric agreement with observed occurrences over score-map and non-conditional baselines, while representing epistemic uncertainty through conditional sampling.

Photoplethysmography (PPG) has become an important modality for continuous cardiovascular monitoring, including atrial fibrillation (AF) detection. However, labeled AF recordings remain limited in many clinical settings, making model adaptation difficult when only limited target data are available. Generative modeling offers a natural way to alleviate this scarcity by synthesizing additional AF signals. Existing approaches, however, mainly generate samples that match the target condition without explicitly modeling how an observed source recording should be transformed, making it difficult to leverage abundant source recordings from a specific population or cohort for targeted augmentation. We introduce PulseFlow, a source-conditioned counterfactual generation framework that combines conditional representation learning with invertible latent transport to edit cardiac rhythm while retaining information from the source. Experiments across two clinical cohorts demonstrate effective rhythm transformation, measurable source correspondence, and improved AF classification under limited labels.

With the growing demand for privacy-preserving and occlusion-resilient human pose recognition (HPR), 5G channel state information (CSI) offers a promising contactless sensing modality by integrating communication and sensing capabilities. However, collecting large-scale synchronized CSI-pose pairs remains costly in practical 5G systems. To address this limitation, we propose StructFlow-HPR, a structured pose-conditioned flow matching framework for generative CSI augmentation. StructFlow-HPR learns a continuous latent transport process from Gaussian noise to real CSI representations under pose guidance, while preserving the receiver-frequency topology of CSI through a reconstruction-preserving autoencoder. A pose-conditioned Transformer is further designed to model the latent velocity field and generate pose-aligned CSI samples via ordinary differential equation sampling. Experiments on real-world 5G sensing data show that StructFlow-HPR can produce realistic CSI-pose pairs and improve downstream HPR performance under limited-data conditions.

We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is sufficient if and only if predicting the response from the reduced covariates incurs no loss in expected score relative to the full covariates. Sufficient dimension reduction thus becomes a risk minimization problem. SRDR jointly trains a dimension reduction map and a generative prediction model by minimizing the energy score, which can be estimated by sampling without density evaluation or adversarial training. The framework extends to multi-environment data and to classification. We prove that the estimated conditional distributions converge in energy distance to the true ones, which implies that the learned representation is asymptotically sufficient. In simulations and applications to CT slice localization, superconductivity, and digit classification, SRDR recovers low-dimensional sufficient structure and matches or outperforms state-of-the-art nonlinear SDR methods in representation quality and predictive performance.

Fast surrogates for tokamak boundary-plasma simulation are typically deterministic regressors mapping a global operating point to a flattened vector of cell values. Near the divertor detachment transition the steady state is not reliably single-valued. A point estimate must average over qualitatively different plasma states, and it arrives with no statement of confidence. Moreover, the flattened vector representation discards the geometric structure of the SOLPS-ITER mesh. This work addresses both problems. We unroll the curvilinear mesh into three fixed-size image tensors whose layout preserves cell adjacency and inverts exactly, letting a convolutional network act on the geometry without loss of information. A conditional flow matching model, well suited to highly sensitive systems, is then trained on this representation. The result is an efficient, scalable surrogate that captures multiple plausible outcomes even at sensitive operating points. Along a gas-puff scan, the predictive distribution splits into a hot and a cold mode across an early regime transition. A further check on synthetic data with an injected bifurcation of known size confirms the model recovers both branches rather than their average.

Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.

Text-controlled time series generation aims to synthesize sequences that follow natural-language descriptions while remaining faithful to real data distributions. Existing paradigms often couple semantic understanding and sequence modeling in a single continuous latent space, lacking explicit local semantic anchors and separation between global continuous attributes and local discrete shapes. As a result, key local structures may be smoothed, missed, or misplaced. We propose Shape Lexicon (ShapeLex), which decouples text-to-sequence generation into discrete symbolization of local shapes and continuous modeling of global attributes. ShapeLex first induces a reusable vocabulary of discrete shape units, such as rises, spikes, and sharp drops, from training data, forming an interpretable symbolic space. An autoregressive generator then selects shapes according to the textual description, adjusts attributes such as position and duration, and composes them in temporal order into a shape skeleton. Finally, a mixture-density scale head models and samples the overall level and volatility to restore realistic global scale. Experiments on twelve public datasets, real user-written text, and downstream forecasting tasks show that ShapeLex generates series that better match real data distributions than existing methods. In addition, paired supervision is automatically synthesized from the learned vocabulary, avoiding annotation costs that grow with dataset size and improving scalability.

Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.

Studying the dynamical behavior of a system often depends on characterizing how it transitions between long-lived states. Because such transitions are rare, observing them usually requires specialized enhanced sampling techniques. Transition Path Sampling (TPS) is a well-established method for generating reactive trajectories, which is simple to implement and does not require the definition of a preconceived reaction coordinate. However, its efficiency is limited by its sequential nature and the resulting correlations between sampled paths. Previous work addressed this limitation by combining TPS with a sampling scheme based on conditioned Boltzmann Generators, a generative machine learning model capable of sampling a given target probability distribution. This approach produces uncorrelated transition paths but relies on an accurate reaction coordinate, which is rarely known in advance. Building on recent advances in committor learning, specifically on the Artificial Intelligence for Molecular Mechanism Discovery (AIMMD) method, in this work we introduce GenAIMMD, an iterative algorithm that actively and self-consistently learns the ideal reaction coordinate (the committor) and trains a conditioned Boltzmann Generator to sample from arbitrary bias windows along it. GenAIMMD thereby provides a correlation-free and fully parallelizable path sampling scheme that does not require prior knowledge of the system's transition mechanism. We apply GenAIMMD to a two-dimensional toy model and a higher-dimensional polymer system. In both cases, GenAIMMD succeeds in training the Boltzmann Generator and learning the committor. Benchmark results show a substantial increase in performance compared to standard TPS.