We introduce Triangular-Reference Schrödinger Bridges for Time Series (TR-SBTS), a conservative extension of the SBTS framework in which the Brownian reference is replaced by an intervalwise frozen, possibly degenerate diffusion reference, triangular across a hierarchy of latent volatility levels. The construction is a single entropy projection on the augmented state space, with the variational constraint imposed jointly across time and the latent levels and unfolded hierarchically by the disintegration of relative entropy. The variational core of SBTS is preserved: the entropy minimiser is the h-transform of the reference, and on each frozen interval the optimal dynamics admit a logarithmic-gradient drift formula on the affine leaves of the active covariance directions, valid even when the frozen covariance is rank-deficient. We establish stability of the frozen approximation and convergence of the corresponding regularised kernel estimators. The construction is realised through a finite-dimensional conditioning map assembled from three complementary reductions of the past -- a block PCR summary, a reference-aware Mahalanobis kernel on past increments induced by the runtime frozen covariance cumulants, and a past-window WLS drift regressor under the same reference metric -- together with a coupled state-covariance bridge step in which each latent level produces a dynamic reference for the level above, summarised by a covariance descriptor; the construction is evaluated on numerical experiments.

We introduce a continuous-time generative modeling framework, motivated by the Chow-Rashevskii theorem, that builds expressive flows from a small set of fixed vector fields and learned scalar controls. Instead of learning an unconstrained high-dimensional vector field, our framework constructs the velocity by modulating fixed vector fields with learned scalar control functions. When the fixed fields are bracket-generating, their Lie algebra spans the ambient space, providing a mechanism for expressive transport with only a small number of learned control channels and offering a parameter-efficient geometric alternative to standard vector-field parameterizations. This decoupled formulation yields a structured and interpretable generative model in which the number of learned scalar output channels can be chosen independently of the ambient dimension. We formulate an expressivity principle showing that, under suitable controllability and well-posedness assumptions, such controlled flows can transport a source distribution to a target distribution. We train the resulting model using a continuous-normalizing-flow likelihood objective and present proof-of-concept experiments on synthetic distributions.

Accurate modeling of aerodynamic loads is essential for understanding and predicting the responses of complex structural systems. However, these models often rely on simplifications of the true physical forces, introducing assumptions that can limit their accuracy. Validating such models becomes particularly challenging in the presence of noisy or incomplete data. To address this, we introduce a probabilistic physics-informed machine learning approach designed to reconstruct the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data during the training process. The efficacy of the approach is demonstrated through the reconstruction of aerodynamic loads on the Great Belt East Bridge, simulated under a linear unsteady assumption. Results show a strong agreement between true and predicted loads, particularly related to root mean squared errors, magnitude, phase angle and peak values of the signals. The method for load reconstructing holds broad applicability, such as modeling validation, future load estimation, and structural damage prognosis.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

OpenAI's CEO, Sam Altman, arrives at the federal courthouse in Oakland, California, on Thursday. OpenAI's CEO, Sam Altman, arrives at the federal courthouse in Oakland, California, on Thursday. Nine-person jury to consider whether AI firm bilked world's richest person and unjustly enriched themselves Closing arguments began on Thursday in Elon Musk's lawsuit against Sam Altman and OpenAI, bringing the weeks-long courtroom battle between the two tech moguls nearer to a decision. A nine-person jury is set to deliberate and return a verdict on whether they believe the AI firm and Altman are liable in the case. The trial, which began last month in an Oakland, California, federal courthouse, has gripped Silicon Valley and featured some of the tech industry's biggest names as witnesses.

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein--Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality--diversity tradeoff. Code is available at: github.com/imbirik/mcb.

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mapping between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM achieves better sample quality than representative baselines while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.

It probably looked as cool as you think. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Gold ligature surrounding the left central incisor and the right lateral incisor on the mandible of an adult male buried in the East Kirk of the parish church of St Nicholas, Aberdeen, Scotland. Breakthroughs, discoveries, and DIY tips sent six days a week. Today, extensive tooth repair or replacement often requires the installation of a dental bridge made from durable resin and metal.

Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples coordinate through shared population statistics to transport probability mass more efficiently? We introduce Mean-Field Path-Integral Diffusion (MF-PID), a framework in which samples are promoted to interacting agents whose drift depends self-consistently on the evolving population density. We identify two analytically tractable regimes: a Linear-Quadratic-Gaussian (LQG) benchmark in which the infinite-dimensional mean-field system reduces to a finite set of Riccati and linear ODEs, and a Gaussian-mixture regime governed by a piecewise-constant protocol that preserves closed-form solvability. For a quadratic interaction potential with schedule βt and zero base drift we prove that the self-consistent MF guidance is the exact linear interpolant between initial and target global means -- a result that holds for arbitrary initial and target densities and any βt. Applied to demand-response control of energy systems, where agents aggregated into an ensemble are energy consumers (e.g. The energy saving is independent of the number of zones per building (d = 1-32 tested), confirming that the linear guidance formula broadcasts a single d-vector with O(d) communication and grows mildly in compute (sub-cubically for d 32, asymptotically O(d3) for d 1). Introduction Generative AI has been transformed by diffusion models, which frame sample generation as a stochastic process steered from noise to data [1-3]. A key structural feature of these models -- shared with other generative models, e.g. Similarly, stochastic optimal transport (SOT) and Schrödinger bridge formulations [6-8] cast distribution matching as an independent-particle path optimization, yielding tractable convolutions of Green functions but discarding inter-particle information; stochastic interpolants [9] construct flexible transport bridges between arbitrary densities via tunable continuous-time stochastic processes, recovering the Schrödinger bridge as a special limit -- again in an independent-particle framework.

Generative models for time-series imputation achieve strong reconstruction accuracy, yet provide no finite-sample reliability guarantees, a critical limitation in power systems where imputed values inform dispatch and planning. We introduce SPLICE (Self-supervised Predictive Latent Inpainting with Conformal Envelopes), a modular framework coupling latent generative imputation with distribution-free, online-adaptive prediction intervals. A JEPA encoder maps daily load segments into a 64-dimensional latent space; a conditional latent bridge with four sampling modes generates candidate gap trajectories; an hourly-conditioned decoder maps back to signal space; and Adaptive Conformal Inference (ACI) wraps the output with coverage-guaranteed prediction bands. The flow-matching variant achieves comparable quality to DDIM in 5--10 ODE steps (5-10x speedup). On thirteen load datasets (nine proprietary, three UCI Electricity, ETTh1), SPLICE achieves the lowest mean Load-only MSE (0.056), winning 9/12 non-degenerate datasets at 91-day gaps and 18/32 across all gap lengths vs. five established baselines, and produces the best CRPS (0.161, -18.3% vs. the strongest competitor). ACI delivers 93--95% empirical coverage, correcting under-coverage failures of up to 7.5 pp observed with static conformal prediction. A pooled JEPA encoder trained on nine feeds transfers to four unseen domains, matching or exceeding per-dataset oracles with only a quick bridge fine-tuning.