In this document, we provide additional details and results to the main paper. The document is structured as follows: A.1 Loss Analysis - Analysis of the unimodal and multimodal latent regularization loss across different distributions and an ablation study on the proposed loss function. A.2 Image Generation - In this section, we compare VQVAE model with our method, provide detailed descriptions of the dataset, network architecture, and implementation details of the image generation experiments in the main paper. A.3 Modelling Discrete Structures - In this section, we describe the experimental and implementation details of the discrete data structure experiments in the main paper. A.5 Additional Qualitative Analysis - More examples of the randomly generated samples of MNIST, FASHIONMNIST, SVHN and CELEBA images.

A.1 Network Architectures We adopt Daformer [17] with Swin-B or MiT-B5 backbone as the base semantic segmentation architecture. For the segmentation head, we utilize the same head as Daformer [17]. The stem module contains one fully-convolutional layers with kernel 3 3 and stride of 2, two fully-convolutional layers with kernel 3 3 and stride of 1, two fully-convolutional layers with kernel 3 3 and stride of 2, and another three fully-convolutional layers with kernel 1 1 and stride of 1 to adjust channels of different feature maps. Level embedding module is defined as metrics with shape 3 dims. The prompt Interactor module contains three fully-convolutional layers with kernel 3 3 and stride of 2 to adjust feature dimensions.

A.1 Algorithm The code is available at https://github.com/mklissa/MOC. A.2 Tabular experiments A.2.1 Implementation Details For our experiments of the FourRooms domain we based our implementation on [Bacon et al., 2016] and ran the experiments for 500 episodes that last a maximum of 1000 steps with goal located in the right hallway. In the first experiment we verify whether learning a fixed set of options can be accelerated by our method. We define this fixed set as the hallway options from Sutton et al. [1999b]. As the policies of these options were deterministic and we use importance sampling, we relax them to stochastic policies where the most likely action is the one leading to a hallway.

This paper presents PolyDiffuse, a novel structured reconstruction algorithm that transforms visual sensor data into polygonal shapes with Diffusion Models (DM), an emerging machinery amid exploding generative AI, while formulating reconstruction as a generation process conditioned on sensor data. The task of structured reconstruction poses two fundamental challenges to DM: 1) A structured geometry is a "set" (e.g., a set of polygons for a floorplan geometry), where a sample of N elements has N! different but equivalent representations, making the denoising highly ambiguous; and 2) A "reconstruction" task has a single solution, where an initial noise needs to be chosen carefully, while any initial noise works for a generation task. Our technical contribution is the introduction of a Guided Set Diffusion Model where 1) the forward diffusion process learns guidance networks to control noise injection so that one representation of a sample remains distinct from its other permutation variants, thus resolving denoising ambiguity; and 2) the reverse denoising process reconstructs polygonal shapes, initialized and directed by the guidance networks, as a conditional generation process subject to the sensor data. We have evaluated our approach for reconstructing two types of polygonal shapes: floorplan as a set of polygons and HD map for autonomous cars as a set of polylines. Through extensive experiments on standard benchmarks, we demonstrate that PolyDiffuse significantly advances the current state of the art and enables broader practical applications. The code and data are available on our project page: https://poly-diffuse.github.io.

V ariable batch size According to our budget decay scheme, the total budget (200 human annotations + 800 GPT -3.5 annotations) allocated for human annotation is 100, 50, 25, 13 (rounded up from

W e are also committed to releasing the code. Implementation details for Stage 2. Our implementation strictly follows the previous work that also In this section, we briefly introduce our tasks. It requires the robot hand to open the door on the table. It requires the robot hand to orient the pen to the target orientation. It requires the robot hand to place the object on the table into the mug. We present the success rates of our six task categories as in Table 1.