Diffusion and flow-based models benefit from simple regression losses, but inference (i.e, producing samples) incurs significant computational overhead because it requires integration. Consistency models address this overhead by directly learning the flow maps along the ODE trajectory, revealing a design space for the learning problem between one-step and many-step approaches. However, existing consistency training methods feature computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce CurlFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. CurlFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics (i.e., those with curl) with stationary point at the desired flow map. On the CIFAR image benchmark, CurlFlow attains a favorable relationship of FID to step count, relative to flow matching, MeanFlow, and several other flow map learning methods.

Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration. Consistency models address this by directly learning the flow maps along the ODE trajectory, opening a design space between one-step and many-step approaches. However, existing methods face computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. SGFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics with a stationary point at the desired flow map. On the CIFAR image benchmark, no single method attains the best FID at every step count: SGFlow attains the best FID at 10 sampling steps and remains competitive with flow matching, Meanflow, and Lagrangian map matching at other step counts, while being the only one with a proven stationary-point guarantee for its stopgrad-based dynamics.

Decision support in fields such as healthcare and finance requires reasoning about treatment timing. Artificial Intelligence holds great potential for supporting such decisions by estimating the causal effect of policies such as medication regimens or resource allocation schedules. However, existing methods for effect estimation are limited in their ability to handle \emph{irregular time}. While treatments and observations in data are often irregularly spaced across time, existing techniques either discretize time, which does scale gracefully, or disregard the effect of treatment time.We present a solution for effect estimation of sequential treatment times called Earliest Disagreement Q-Evaluation (EDQ). The method is based on Dynamic Programming and is compatible with flexible sequence models, such as transformers. EDQ provides accurate estimates under standard assumptions. We validate the approach through experiments on a survival time prediction task.

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than standard diffusion models, makes possible a modular study of various design choices impacting generative models built on dynamical transport: learning in discrete or continuous time, the objective function, the interpolant that connects the distributions, and deterministic or stochastic sampling. By carefully introducing the above ingredients, SiT surpasses DiT uniformly across model sizes on the conditional ImageNet 256x256 and 512x512 benchmark using the exact same model structure, number of parameters, and GFLOPs. By exploring various diffusion coefficients, which can be tuned separately from learning, SiT achieves an FID-50K score of 2.06 and 2.62, respectively.

BACKGROUND:Prediction of drug-induced long QT syndrome (diLQTS) is of critical importance given its association with torsades de pointes. There is no reliable method for the outpatient prediction of diLQTS. OBJECTIVES:This study sought to evaluate the use of a convolutional neural network (CNN) applied to electrocardiograms (ECGs) to predict diLQTS in an outpatient population. METHODS:We identified all adult outpatients newly prescribed a QT-prolonging medication between January 1, 2003, and March 31, 2022, who had a 12-lead sinus ECG in the preceding 6 months. Using risk factor data and the ECG signal as inputs, the CNN QTNet was implemented in TensorFlow to predict diLQTS. RESULTS:Models were evaluated in a held-out test dataset of 44,386 patients (57% female) with a median age of 62 years. Compared with 3 other models relying on risk factors or ECG signal or baseline QTc alone, QTNet achieved the best (P < 0.001) performance with a mean area under the curve of 0.802 (95% CI: 0.786-0.818). In a survival analysis, QTNet also had the highest inverse probability of censorship-weighted area under the receiver-operating characteristic curve at day 2 (0.875; 95% CI: 0.848-0.904) and up to 6 months. In a subgroup analysis, QTNet performed best among males and patients ≤50 years or with baseline QTc <450 ms. In an external validation cohort of solely suburban outpatient practices, QTNet similarly maintained the highest predictive performance. CONCLUSIONS:An ECG-based CNN can accurately predict diLQTS in the outpatient setting while maintaining its predictive performance over time. In the outpatient setting, our model could identify higher-risk individuals who would benefit from closer monitoring.

Aims Myocardial infarction and heart failure are major cardiovascular diseases that affect millions of people in the USA with morbidity and mortality being highest among patients who develop cardiogenic shock. Early recognition of cardiogenic shock allows prompt implementation of treatment measures. Our objective is to develop a new dynamic risk score, called CShock, to improve early detection of cardiogenic shock in the cardiac intensive care unit (ICU).Methods and results We developed and externally validated a deep learning-based risk stratification tool, called CShock, for patients admitted into the cardiac ICU with acute decompensated heart failure and/or myocardial infarction to predict the onset of cardiogenic shock. We prepared a cardiac ICU dataset using the Medical Information Mart for Intensive Care-III database by annotating with physician-adjudicated outcomes. This dataset which consisted of 1500 patients with 204 having cardiogenic/mixed shock was then used to train CShock. The features used to train the model for CShock included patient demographics, cardiac ICU admission diagnoses, routinely measured laboratory values and vital signs, and relevant features manually extracted from echocardiogram and left heart catheterization reports. We externally validated the risk model on the New York University (NYU) Langone Health cardiac ICU database which was also annotated with physician-adjudicated outcomes. The external validation cohort consisted of 131 patients with 25 patients experiencing cardiogenic/mixed shock. CShock achieved an area under the receiver operator characteristic curve (AUROC) of 0.821 (95% CI 0.792-0.850). CShock was externally validated in the more contemporary NYU cohort and achieved an AUROC of 0.800 (95% CI 0.717-0.884), demonstrating its generalizability in other cardiac ICUs. Having an elevated heart rate is most predictive of cardiogenic shock development based on Shapley values. The other top 10 predictors are having an admission diagnosis of myocardial infarction with ST-segment elevation, having an admission diagnosis of acute decompensated heart failure, Braden Scale, Glasgow Coma Scale, blood urea nitrogen, systolic blood pressure, serum chloride, serum sodium, and arterial blood pH.Conclusion The novel CShock score has the potential to provide automated detection and early warning for cardiogenic shock and improve the outcomes for millions of patients who suffer from myocardial infarction and heart failure. Graphical Abstract

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of the future system state given its current state. To this end, we leverage the framework of stochastic interpolants, which facilitates the construction of a generative model between an arbitrary base distribution and the target. We design a fictitious, non-physical stochastic dynamics that takes as initial condition the current system state and produces as output a sample from the target conditional distribution in finite time and without bias. This process therefore maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. We prove that the drift coefficient entering the stochastic differential equation (SDE) achieving this task is non-singular, and that it can be learned efficiently by square loss regression over the time-series data. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a Föllmer process. We highlight the utility of our approach on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes and video prediction on the KTH and CLEVRER datasets.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Contrastive learning methods, such as CLIP, leverage naturally paired data-for example, images and their corresponding text captions-to learn general representations that transfer efficiently to downstream tasks. While such approaches are generally applied to two modalities, domains such as robotics, healthcare, and video need to support many types of data at once. We show that the pairwise application of CLIP fails to capture joint information between modalities, thereby limiting the quality of the learned representations. To address this issue, we present Symile, a simple contrastive learning approach that captures higher-order information between any number of modalities. Symile provides a flexible, architecture-agnostic objective for learning modality-specific representations. To develop Symile's objective, we derive a lower bound on total correlation, and show that Symile representations for any set of modalities form a sufficient statistic for predicting the remaining modalities. Symile outperforms pairwise CLIP, even with modalities missing in the data, on cross-modal classification and retrieval across several experiments including on an original multilingual dataset of 33M image, text and audio samples and a clinical dataset of chest X-rays, electrocardiograms, and laboratory measurements. All datasets and code used in this work are publicly available at https://github.com/rajesh-lab/symile.

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution, limiting the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this inference process to generate samples. The choice of inference diffusion affects both likelihoods and sample quality as it is tied to the generative model. Recent work in DBGMs has applied the principle of improving generative models with the use of auxiliary variables, leading to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study linear Multivariate Diffusion Models (MDMs). First, for any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDM likelihood, without requiring any model-specific analysis. Next, we demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over the set of linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST and CIFAR10 datasets. We achieve improved bits-per-dim bounds using the new diffusion, compared to the existing likelihood-trained VPSDE. We additionally connect the existing CLD objective to the likelihood lower-bound.

Myocardial infarction and heart failure are major cardiovascular diseases that affect millions of people in the US. The morbidity and mortality are highest among patients who develop cardiogenic shock. Early recognition of cardiogenic shock is critical. Prompt implementation of treatment measures can prevent the deleterious spiral of ischemia, low blood pressure, and reduced cardiac output due to cardiogenic shock. However, early identification of cardiogenic shock has been challenging due to human providers' inability to process the enormous amount of data in the cardiac intensive care unit (ICU) and lack of an effective risk stratification tool. We developed a deep learning-based risk stratification tool, called CShock, for patients admitted into the cardiac ICU with acute decompensated heart failure and/or myocardial infarction to predict onset of cardiogenic shock. To develop and validate CShock, we annotated cardiac ICU datasets with physician adjudicated outcomes. CShock achieved an area under the receiver operator characteristic curve (AUROC) of 0.820, which substantially outperformed CardShock (AUROC 0.519), a well-established risk score for cardiogenic shock prognosis. CShock was externally validated in an independent patient cohort and achieved an AUROC of 0.800, demonstrating its generalizability in other cardiac ICUs.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

Spurious correlations allow flexible models to predict well during training but poorly on related test populations. Recent work has shown that models that satisfy particular independencies involving correlation-inducing nuisance variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive MMD estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Deep generative models (DGMs) seem a natural fit for detecting out-of-distribution (OOD) inputs, but such models have been shown to assign higher probabilities or densities to OOD images than images from the training distribution. In this work, we explain why this behavior should be attributed to model misestimation. We first prove that no method can guarantee performance beyond random chance without assumptions on which out-distributions are relevant. We then interrogate the typical set hypothesis, the claim that relevant out-distributions can lie in high likelihood regions of the data distribution, and that OOD detection should be defined based on the data distribution's typical set. We highlight the consequences implied by assuming support overlap between in- and out-distributions, as well as the arbitrariness of the typical set for OOD detection. Our results suggest that estimation error is a more plausible explanation than the misalignment between likelihood-based OOD detection and out-distributions of interest, and we illustrate how even minimal estimation error can lead to OOD detection failures, yielding implications for future work in deep generative modeling and OOD detection.

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.

Recurrent Neural Networks (RNNs) facilitate prediction and generation of structured temporal data such as text and sound. However, training RNNs is hard. Vanishing gradients cause difficulties for learning long-range dependencies. Hidden states can explode for long sequences and send unbounded gradients to model parameters, even when hidden-to-hidden Jacobians are bounded. Models like the LSTM and GRU use gates to bound their hidden state, but most choices of gating functions lead to saturating gradients that contribute to, instead of alleviate, vanishing gradients. Moreover, performance of these models is not robust across random initializations. In this work, we specify desiderata for sequence models. We develop one model that satisfies them and that is capable of learning long-term dependencies, called GATO. GATO is constructed so that part of its hidden state does not have vanishing gradients, regardless of sequence length. We study GATO on copying and arithmetic tasks with long dependencies and on modeling intensive care unit and language data. Training GATO is more stable across random seeds and learning rates than GRUs and LSTMs. GATO solves these tasks using an order of magnitude fewer parameters.

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows practitioners to directly optimize calibration and strike a desired balance between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.