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Generative adversial network (GAN) is a type of generative model that maps a high-dimensional noise to samples in target distribution. However, the dimension of noise required in GAN is not well understood. Previous approaches view GAN as a mapping from a continuous distribution to another continous distribution. In this paper, we propose to view GAN as a discrete sampler instead. From this perspective, we build a connection between the minimum noise required and the bits to losslessly compress the images. Furthermore, to understand the behaviour of GAN when noise dimension is limited, we propose divergence-entropy trade-off. This trade-off depicts the best divergence we can achieve when noise is limited. And as rate distortion trade-off, it can be numerically solved when source distribution is known. Finally, we verifies our theory with experiments on image generation., Comment: ICME24

Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_{\theta}(X_0|y)$, with a predefined diffusion model $p_{\theta}(X_0)$, an operator $f(\cdot)$, and a measurement $y=f(x'_0)$ derived from an unknown image $x'_0$. Existing DIS estimate the conditional score function by evaluating $f(\cdot)$ with an approximated posterior sample drawn from $p_{\theta}(X_0|X_t)$. However, most prior approximations rely on the posterior means, which may not lie in the support of the image distribution, thereby potentially diverge from the appearance of genuine images. Such out-of-support samples may significantly degrade the performance of the operator $f(\cdot)$, particularly when it is a neural network. In this paper, we introduces a novel approach for posterior approximation that guarantees to generate valid samples within the support of the image distribution, and also enhances the compatibility with neural network-based operators $f(\cdot)$. We first demonstrate that the solution of the Probability Flow Ordinary Differential Equation (PF-ODE) with an initial value $x_t$ yields an effective posterior sample $p_{\theta}(X_0|X_t=x_t)$. Based on this observation, we adopt the Consistency Model (CM), which is distilled from PF-ODE, for posterior sampling. Furthermore, we design a novel family of DIS using only CM. Through extensive experiments, we show that our proposed method for posterior sample approximation substantially enhance the effectiveness of DIS for neural network operators $f(\cdot)$ (e.g., in semantic segmentation). Additionally, our experiments demonstrate the effectiveness of the new CM-based inversion techniques. The source code is provided in the supplementary material.

The physical design process of large-scale designs is a time-consuming task, often requiring hours to days to complete, with routing being the most critical and complex step. As the the complexity of Integrated Circuits (ICs) increases, there is an increased demand for accurate routing quality prediction. Accurate congestion prediction aids in identifying design flaws early on, thereby accelerating circuit design and conserving resources. Despite the advancements in current congestion prediction methodologies, an essential aspect that has been largely overlooked is the spatial label-correlation between different grids in congestion prediction. The spatial label-correlation is a fundamental characteristic of circuit design, where the congestion status of a grid is not isolated but inherently influenced by the conditions of its neighboring grids. In order to fully exploit the inherent spatial label-correlation between neighboring grids, we propose a novel approach, {\ours}, i.e., VAriational Label-Correlation Enhancement for Congestion Prediction, which considers the local label-correlation in the congestion map, associating the estimated congestion value of each grid with a local label-correlation weight influenced by its surrounding grids. {\ours} leverages variational inference techniques to estimate this weight, thereby enhancing the regression model's performance by incorporating spatial dependencies. Experiment results validate the superior effectiveness of {\ours} on the public available \texttt{ISPD2011} and \texttt{DAC2012} benchmarks using the superblue circuit line.