Diffusion models excel in generating high-quality images. However, current diffusion models struggle to produce reliable images without guidance methods, such as classifier-free guidance (CFG). Are guidance methods truly necessary? Observing that noise obtained via diffusion inversion can reconstruct high-quality images without guidance, we focus on the initial noise of the denoising pipeline. By mapping Gaussian noise to `guidance-free noise', we uncover that small low-magnitude low-frequency components significantly enhance the denoising process, removing the need for guidance and thus improving both inference throughput and memory. Expanding on this, we propose \ours, a novel method that replaces guidance methods with a single refinement of the initial noise. This refined noise enables high-quality image generation without guidance, within the same diffusion pipeline. Our noise-refining model leverages efficient noise-space learning, achieving rapid convergence and strong performance with just 50K text-image pairs. We validate its effectiveness across diverse metrics and analyze how refined noise can eliminate the need for guidance. See our project page: https://cvlab-kaist.github.io/NoiseRefine/.

The real-world traffic networks undergo expansion through the installation of new sensors, implying that the traffic patterns continually evolve over time. Incrementally training a model on the newly added sensors would make the model forget the past knowledge, i.e., catastrophic forgetting, while retraining the model on the entire network to capture these changes is highly inefficient. To address these challenges, we propose a novel Traffic Forecasting Mixture of Experts (TFMoE) for traffic forecasting under evolving networks. The main idea is to segment the traffic flow into multiple homogeneous groups, and assign an expert model responsible for a specific group. This allows each expert model to concentrate on learning and adapting to a specific set of patterns, while minimizing interference between the experts during training, thereby preventing the dilution or replacement of prior knowledge, which is a major cause of catastrophic forgetting. Through extensive experiments on a real-world long-term streaming network dataset, PEMSD3-Stream, we demonstrate the effectiveness and efficiency of TFMoE.

Accurate traffic flow forecasting is a crucial research topic in transportation management. However, it is a challenging problem due to rapidly changing traffic conditions, high nonlinearity of traffic flow, and complex spatial and temporal correlations of road networks. Most existing studies either try to capture the spatial dependencies between roads using the same semantic graph over different time steps, or assume all sensors on the roads are equally likely to be connected regardless of the distance between them. However, we observe that the spatial dependencies between roads indeed change over time, and two distant roads are not likely to be helpful to each other when predicting the traffic flow, both of which limit the performance of existing studies. In this paper, we propose Temporal Graph Learning Recurrent Neural Network (TGLRN) to address these problems. More precisely, to effectively model the nature of time series, we leverage Recurrent Neural Networks (RNNs) to dynamically construct a graph at each time step, thereby capturing the time-evolving spatial dependencies between roads (i.e., microscopic view). Simultaneously, we provide the Adaptive Structure Information to the model, ensuring that close and consecutive sensors are considered to be more important for predicting the traffic flow (i.e., macroscopic view). Furthermore, to endow TGLRN with robustness, we introduce an edge sampling strategy when constructing the graph at each time step, which eventually leads to further improvements on the model performance. Experimental results on four commonly used real-world benchmark datasets show the effectiveness of TGLRN.

B-spline-based trajectory optimization is widely used for robot navigation due to its computational efficiency and convex-hull property (ensures dynamic feasibility), especially as quadrotors, which have circular body shapes (enable efficient movement) and freedom to move each axis (enables convex-hull property utilization). However, using the B-spline curve for trajectory optimization is challenging for autonomous vehicles (AVs) because of their vehicle kinodynamics (rectangular body shapes and constraints to move each axis). In this study, we propose a novel trajectory optimization approach for AVs to circumvent this difficulty using an incremental path flattening (IPF), a disc type swept volume (SV) estimation method, and kinodynamic feasibility constraints. IPF is a new method that can find a collision-free path for AVs by flattening path and reducing SV using iteratively increasing curvature penalty around vehicle collision points. Additionally, we develop a disc type SV estimation method to reduce SV over-approximation and enable AVs to pass through a narrow corridor efficiently. Furthermore, a clamped B-spline curvature constraint, which simplifies a B-spline curvature constraint, is added to dynamical feasibility constraints (e.g., velocity and acceleration) for obtaining the kinodynamic feasibility constraints. Our experimental results demonstrate that our method outperforms state-of-the-art baselines in various simulated environments. We also conducted a real-world experiment using an AV, and our results validate the simulated tracking performance of the proposed approach.

We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two sub-networks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram-Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.