Ziran Zhu

Tongda Xu, Ziran Zhu, Dailan He et al.

Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fréchet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.

Tongda Xu, Ziran Zhu, Jian Li et al.

Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_θ(X_0|y)$, with a predefined diffusion model $p_θ(X_0)$, 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 $p_θ(X_0|X_t)$. 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 $p_θ(X_0|X_t=x_t)$. 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.

Ziran Zhu, Tongda Xu, Ling Li et al.

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.