Flat minima, known to enhance generalization and robustness in supervised learning, remain largely unexplored in generative models. In this work, we systematically investigate the role of loss surface flatness in generative models, both theoretically and empirically, with a particular focus on diffusion models. We establish a theoretical claim that flatter minima improve robustness against perturbations in target prior distributions, leading to benefits such as reduced exposure bias -- where errors in noise estimation accumulate over iterations -- and significantly improved resilience to model quantization, preserving generative performance even under strong quantization constraints. We further observe that Sharpness-Aware Minimization (SAM), which explicitly controls the degree of flatness, effectively enhances flatness in diffusion models even surpassing the indirectly promoting flatness methods -- Input Perturbation (IP) which enforces the Lipschitz condition, ensembling-based approach like Stochastic Weight Averaging (SWA) and Exponential Moving Average (EMA) -- are less effective. Through extensive experiments on CIFAR-10, LSUN Tower, and FFHQ, we demonstrate that flat minima in diffusion models indeed improve not only generative performance but also robustness.

Federated learning (FL) enables decentralized training while preserving data privacy, yet existing FL benchmarks address relatively simple classification tasks, where each sample is annotated with a one-hot label. However, little attention has been paid to demonstrating an FL benchmark that handles complicated semantics, where each sample encompasses diverse semantic information, such as relations between objects. Because the existing benchmarks are designed to distribute data in a narrow view of a single semantic, managing the complicated semantic heterogeneity across clients when formalizing FL benchmarks is non-trivial. In this paper, we propose a benchmark process to establish an FL benchmark with controllable semantic heterogeneity across clients: two key steps are (i) data clustering with semantics and (ii) data distributing via controllable semantic heterogeneity across clients. As a proof of concept, we construct a federated PSG benchmark, demonstrating the efficacy of the existing PSG methods in an FL setting with controllable semantic heterogeneity of scene graphs. We also present the effectiveness of our benchmark by applying robust federated learning algorithms to data heterogeneity to show increased performance. To our knowledge, this is the first benchmark framework that enables federated learning and its evaluation for multi-semantic vision tasks under the controlled semantic heterogeneity. Our code is available at https://github.com/Seung-B/FL-PSG .

Albeit the success of federated learning (FL) in decentralized training, bolstering the generalization of models by overcoming heterogeneity across clients still remains a huge challenge. To aim at improved generalization of FL, a group of recent works pursues flatter minima of models by employing sharpness-aware minimization in the local training at the client side. However, we observe that the global model, i.e., the aggregated model, does not lie on flat minima of the global objective, even with the effort of flatness searching in local training, which we define as flatness discrepancy. By rethinking and theoretically analyzing flatness searching in FL through the lens of the discrepancy problem, we propose a method called Federated Learning for Global Flatness (FedGF) that explicitly pursues the flatter minima of the global models, leading to the relieved flatness discrepancy and remarkable performance gains in the heterogeneous FL benchmarks.

Most path planning algorithms for a marine surface vehicle in the ocean environment have been developed only for a 2-D (x;y) plane without considering the vehicle heading angle. As a result, the vehicle has a difficulty in following the path correctly. In this paper, we propose a limit-cycle circle set that applies to the Theta* algorithm. The minimum turning radius of a marine surface vehicle is calculated using a limit-cycle circle set, and circles of this radius is used to generate a configuration space of an occupancy grid map. After applying Theta* to this configuration space, the limit-cycle circle set is also applied to the start and end nodes to find the appropriate path with specified heading angles. The benefit of this algorithm is its fast computation time compared to other 3-D (x;y;θ) path planning algorithms, along with the fact that it can be applied to the 3-D kinematic state of the vehicle. We simulate the proposed algorithm and compare it with 3-D A* and 3-D A* with post smoothing algorithms.