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Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Imitation learning with diffusion models has advanced robotic control by capturing the multi-modal action distributions. However, existing methods typically treat observations only as high-level conditions to the denoising network, rather…

Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically…

Transition Matching (TM) is an emerging paradigm for generative modeling that generalizes diffusion and flow-matching models as well as continuous-state autoregressive models. TM, similar to previous paradigms, gradually transforms noise…

Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE)…

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…

Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…

Offline decision-making via diffusion models often produces trajectories that are misaligned with system dynamics, limiting their reliability for control. We propose Model Predictive Diffuser (MPDiffuser), a compositional diffusion…

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…

This paper proposes a robust control design method using reinforcement-learning for controlling partially-unknown dynamical systems under uncertain conditions. The method extends the optimal reinforcement-learning algorithm with a new…

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…

Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…

Diffusion models generate samples through an iterative denoising process, guided by a neural network. While training the denoiser on real-world data is computationally demanding, the sampling procedure itself is more flexible. This…

Intelligent surgical robots have the potential to revolutionize clinical practice by enabling more precise and automated surgical procedures. However, the automation of such robot for surgical tasks remains under-explored compared to recent…

Motion prediction is a challenging problem in autonomous driving as it demands the system to comprehend stochastic dynamics and the multi-modal nature of real-world agent interactions. Diffusion models have recently risen to prominence, and…

Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…

Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…