Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solvers

• URL: http://arxiv.org/abs/2403.12063v2
• Date: Sat, 1 Jun 2024 10:54:50 GMT
• Title: Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solvers
• Authors: Tongda Xu, Ziran Zhu, Jian Li, Dailan He, Yuanyuan Wang, Ming Sun, Ling Li, Hongwei Qin, Yan Wang, Jingjing Liu, Ya-Qin Zhang,
• Abstract summary: Previous approximations rely on the posterior means, which may not lie in the support of the image distribution. We introduce a novel approach for posterior approximation that guarantees to generate valid samples within the support of the image distribution.
• Score: 28.678613691787096
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat [49.1574468325115]
  This paper presents explicit non-asymptotic bounds on the forward diffusion error in total variation (TV) We parametrise multi-modal data distributions in terms of the distance $R$ to their furthest modes and consider forward diffusions with additive and multiplicative noise.
  arXiv  Detail & Related papers  (2024-08-25T10:28:31Z)
• A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models [45.60426164657739]
  We develop non-asymptotic convergence theory for a diffusion-based sampler. We prove that $d/varepsilon$ are sufficient to approximate the target distribution to within $varepsilon$ total-variation distance. Our results also characterize how $ell$ score estimation errors affect the quality of the data generation processes.
  arXiv  Detail & Related papers  (2024-08-05T09:02:24Z)
• Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
  This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$. We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
  arXiv  Detail & Related papers  (2024-05-31T16:18:46Z)
• Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions [11.222970035173372]
  kernel-based score estimator achieves an optimal mean square error of $widetildeOleft(n-1 t-fracd+22(tfracd2 vee 1)right) We show that a kernel-based score estimator achieves an optimal mean square error of $widetildeOleft(n-1/2 t-fracd4right)$ upper bound for the total variation error of the distribution of the sample generated by the diffusion model under a mere sub-Gaussian
  arXiv  Detail & Related papers  (2024-02-23T20:51:31Z)
• Diffusion Posterior Sampling is Computationally Intractable [9.483130965295324]
  Posterior sampling is useful for tasks such as inpainting, super-resolution, and MRI reconstruction. We show that posterior sampling is emphcomputationally intractable: under the most basic assumption in cryptography, that one-way functions exist. We also show that the exponential-time rejection sampling is essentially optimal under the stronger plausible assumption that there are one-way functions that take exponential time to invert.
  arXiv  Detail & Related papers  (2024-02-20T05:28:13Z)
• Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories [70.90012822736988]
  Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to intrinsic data structures. This paper introduces a relaxed assumption that input data are concentrated around a subset of $mathbbRd$ denoted by $mathcalS$, and the intrinsic dimension $mathcalS$ can be characterized by a new complexity notation -- effective Minkowski dimension.
  arXiv  Detail & Related papers  (2023-06-26T17:13:31Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Convergence for score-based generative modeling with polynomial complexity [9.953088581242845]
  We prove the first convergence guarantees for the core mechanic behind Score-based generative modeling. Compared to previous works, we do not incur error that grows exponentially in time or that suffers from a curse of dimensionality. We show that a predictor-corrector gives better convergence than using either portion alone.
  arXiv  Detail & Related papers  (2022-06-13T14:57:35Z)
• Approximate Function Evaluation via Multi-Armed Bandits [51.146684847667125]
  We study the problem of estimating the value of a known smooth function $f$ at an unknown point $boldsymbolmu in mathbbRn$, where each component $mu_i$ can be sampled via a noisy oracle. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-delta$ returns an $epsilon$ accurate estimate of $f(boldsymbolmu)$.
  arXiv  Detail & Related papers  (2022-03-18T18:50:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.