Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODEand SDE-based solvers reveals complementary weaknesses: ODE solvers accumulate irreducible gradient error along deterministic trajectories, while SDE methods suffer from amplified discretization errors when the step budget is limited. Building upon this insight, we introduce AdaSDE, a novel single-step SDE solver that aims to unify the efficiency of ODEs with the error resilience of SDEs. Specifically, we introduce a single per-step learnable coefficient, estimated via lightweight distillation, which dynamically regulates the error correction strength to accelerate diffusion sampling. Notably, our framework can be integrated with existing solvers to enhance their capabilities. Extensive experiments demonstrate state-of-the-art performance: at 5 NFE, AdaSDE achieves FID scores of 4.18 on CIFAR-10, 8.05 on FFHQ and 6.96 on LSUN Bedroom.

Mediation analysis has traditionally focused on outcome-level summary contrasts, such as mean effects, which may obscure substantial distributional changes induced by complex and nonlinear causal mechanisms. We propose Distributional Causal Mediation Analysis (DCMA), a generative learning framework for identifying and estimating treatment effects on entire outcome distributions transmitted through multiple mediators. DCMA learns conditional generative models for the mediators and the outcome, recovering the relevant conditional distributions from observational data. Leveraging the identification formulas, it reconstructs interventional outcome distributions via Monte Carlo forward simulation by noise resampling, enabling the capture of both classical summary effects and rich distributional contrasts such as energy distance and the Wasserstein distance. Analytical error bounds are derived to decompose how estimation errors in the learned conditional models propagate to the reconstructed interventional outcome distributions. The empirical effectiveness of DCMA is demonstrated through numerical experiments and real-world data applications.

Learning with an objective to minimize the mismatch with a reference distribution has been shown to be useful for generative modeling and imitation learning. In this paper, we investigate whether one such objective, the Wasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectively for reinforcement learning (RL) tasks. Specifically, this paper focuses on goal-conditioned reinforcement learning where the idealized (unachievable) target distribution has full measure at the goal. This paper introduces a quasimetric specific to Markov Decision Processes (MDPs) and uses this quasimetric to estimate the above Wasserstein-1 distance. It further shows that the policy that minimizes this Wasserstein-1 distance is the policy that reaches the goal in as few steps as possible. Our approach, termed Adversarial Intrinsic Motivation (AIM), estimates this Wasserstein-1 distance through its dual objective and uses it to compute a supplemental reward function. Our experiments show that this reward function changes smoothly with respect to transitions in the MDP and directs the agent's exploration to find the goal efficiently. Additionally, we combine AIM with Hindsight Experience Replay (HER) and show that the resulting algorithm accelerates learning significantly on several simulated robotics tasks when compared to other rewards that encourage exploration or accelerate learning.

In thispaper,weinvestigatewhether onesuchobjective,theWasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectivelyforreinforcement learning (RL)tasks.

In recent years, model-free reinforcement learning (MFRL) has achieved tremendous success on a wide range of simulated domains, e .

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph.

Learning with an objective to minimize the mismatch with a reference distribution has been shown to be useful for generative modeling and imitation learning. In this paper, we investigate whether one such objective, the Wasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectively for reinforcement learning (RL) tasks. Specifically, this paper focuses on goal-conditioned reinforcement learning where the idealized (unachievable) target distribution has full measure at the goal. This paper introduces a quasimetric specific to Markov Decision Processes (MDPs) and uses this quasimetric to estimate the above Wasserstein-1 distance. It further shows that the policy that minimizes this Wasserstein-1 distance is the policy that reaches the goal in as few steps as possible. Our approach, termed Adversarial Intrinsic Motivation (AIM), estimates this Wasserstein-1 distance through its dual objective and uses it to compute a supplemental reward function. Our experiments show that this reward function changes smoothly with respect to transitions in the MDP and directs the agent's exploration to find the goal efficiently. Additionally, we combine AIM with Hindsight Experience Replay (HER) and show that the resulting algorithm accelerates learning significantly on several simulated robotics tasks when compared to other rewards that encourage exploration or accelerate learning.

Electrocardiography (ECG) signals are frequently degraded by noise, limiting their clinical reliability in both conventional and wearable settings. Existing methods for addressing ECG noise, relying on artifact classification or denoising, are constrained by annotation inconsistencies and poor generalizability. Here, we address these limitations by reframing ECG noise quantification as an anomaly detection task. We propose a diffusion-based framework trained to model the normative distribution of clean ECG signals, identifying deviations as noise without requiring explicit artifact labels. To robustly evaluate performance and mitigate label inconsistencies, we introduce a distribution-based metric using the Wasserstein-1 distance ($W_1$). Our model achieved a macro-average $W_1$ score of 1.308, outperforming the next-best method by over 48\%. External validation confirmed strong generalizability, facilitating the exclusion of noisy segments to improve diagnostic accuracy and support timely clinical intervention. This approach enhances real-time ECG monitoring and broadens ECG applicability in digital health technologies.