When CondInstanceNorm++ is added, we name them "CondResBlock" and "CondRefineBlock" We use the ELU activation function [25] throughout all architectures. The latter is configured according to Technique 1-4. The learning rates and batch sizes are provided in Appendix B.1 and Table 4. EMA with momentum 0.9 to smooth the curves in Figure 1. We can interpolate between two different samples from NCSN/NCSNv2 via interpolating the Gaussian random noise injected by annealed Langevin dynamics. As indicated by Figs. 4 and 8, EMA can stabilize training and remove sample FID scores should be interpreted with caution because they may not align well with human judgement.

We thank all the reviewers for providing valuable feedback in this time of stress. We will include these new results in the revision. NCSN (CIFAR-10) NCSNv2 (CIFAR-10) NCSN (CelebA) NCSNv2 (CelebA) FID 27.44 10.31 17.57 9.69 [R1] Is the model memorizing data (like the Eiffel towers in Figure 1)? NCSNv2 uses the new architecture and the others use the old one. We will incorporate your suggestions in the revision.

However, it is an open question how these noise scales should be chosen.

We thank all the reviewers for providing valuable feedback in this time of stress. We will include these new results in the revision. NCSN (CIFAR-10) NCSNv2 (CIFAR-10) NCSN (CelebA) NCSNv2 (CelebA) FID 27.44 10.31 17.57 9.69 [R1] Is the model memorizing data (like the Eiffel towers in Figure 1)? NCSNv2 uses the new architecture and the others use the old one. We will incorporate your suggestions in the revision.

However, the empirical performance of the proposed approach shows huge advantage over NCSN. Can the author elaborate what makes this difference? To my knowledge, the difference are The number of noise-levels (denoted as L): For the diffusion model, L 1000. The scheduling sequence of variance (denoted as beta_t, which is the \sigma 2 in NCSN): For the diffusion model, beta_1 1e-4, beta_T 0.02, and linear schedule is employed. For NCSN, they consider the geometric sequence, and beta_T is much larger for NCSNv2.

Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model performance varies with model size and trajectory temporal resolution. In addition, a performance benchmark is designed to assess the generative model's usefulness for trajectory design, conduct model performance comparisons, and lay the groundwork for evaluating different generative models for trajectory design beyond diffusion. The results of this analysis showcase several useful properties of diffusion models that, when taken together, can enable a future system for generative trajectory design powered by diffusion models. INTRODUCTION Diffusion models are a type of generative model that have achieved state-of-the-art performance across creative and scientific domains. Concerning trajectory design, diffusion models have shown promising results in robotics. Janner et al. propose combining diffusion models with reinforcement learning techniques to develop flexible trajectory planning strategies.

Score-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32 32), and can be unstable under some settings. We provide a new theoretical analysis of learning and sampling from score-based models in high dimensional spaces, explaining existing failure modes and motivating new solutions that generalize across datasets. To enhance stability, we also propose to maintain an exponential moving average of model weights. With these improvements, we can scale scorebased generative models to various image datasets, with diverse resolutions ranging from 64 64 to 256 256. Our score-based models can generate high-fidelity samples that rival best-in-class GANs on various image datasets, including CelebA, FFHQ, and several LSUN categories.