This study addresses the challenges in parameter estimation of stochastic differential equations driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious diseases. Previous research highlighted the potential of LSTM networks in estimating parameters of alpha stable Levy driven SDEs but faced limitations including high time complexity and constraints of the LSTM chaining property. To mitigate these issues, we introduce the PEnet, a novel CNN-LSTM-based three-stage model that offers an end to end approach with superior accuracy and adaptability to varying data structures, enhanced inference speed for long sequence observations through initial data feature condensation by CNN, and high generalization capability, allowing its application to various complex SDE scenarios. Experiments on synthetic datasets confirm PEnet significant advantage in estimating SDE parameters associated with noise characteristics, establishing it as a competitive method for SDE parameter estimation in the presence of Levy noise.

As pretrained text-to-image diffusion models become increasingly powerful, recent efforts have been made to distill knowledge from these text-to-image pretrained models for optimizing a text-guided 3D model. Most of the existing methods generate a holistic 3D model from a plain text input. This can be problematic when the text describes a complex scene with multiple objects, because the vectorized text embeddings are inherently unable to capture a complex description with multiple entities and relationships. Holistic 3D modeling of the entire scene further prevents accurate grounding of text entities and concepts. To address this limitation, we propose GraphDreamer, a novel framework to generate compositional 3D scenes from scene graphs, where objects are represented as nodes and their interactions as edges. By exploiting node and edge information in scene graphs, our method makes better use of the pretrained text-to-image diffusion model and is able to fully disentangle different objects without image-level supervision. To facilitate modeling of object-wise relationships, we use signed distance fields as representation and impose a constraint to avoid inter-penetration of objects. To avoid manual scene graph creation, we design a text prompt for ChatGPT to generate scene graphs based on text inputs. We conduct both qualitative and quantitative experiments to validate the effectiveness of GraphDreamer in generating high-fidelity compositional 3D scenes with disentangled object entities.

Depth completion, which aims to generate high-quality dense depth maps from sparse depth maps, has attracted increasing attention in recent years. Previous work usually employs RGB images as guidance, and introduces iterative spatial propagation to refine estimated coarse depth maps. However, most of the propagation refinement methods require several iterations and suffer from a fixed receptive field, which may contain irrelevant and useless information with very sparse input. In this paper, we address these two challenges simultaneously by revisiting the idea of deformable convolution. We propose an effective architecture that leverages deformable kernel convolution as a single-pass refinement module, and empirically demonstrate its superiority. To better understand the function of deformable convolution and exploit it for depth completion, we further systematically investigate a variety of representative strategies. Our study reveals that, different from prior work, deformable convolution needs to be applied on an estimated depth map with a relatively high density for better performance. We evaluate our model on the large-scale KITTI dataset and achieve state-of-the-art level performance in both accuracy and inference speed. Our code is available at https://github.com/AlexSunNik/ReDC.