Inverse Design for Conditional Distribution Matching

• URL: http://arxiv.org/abs/2605.09439v1
• Date: Sun, 10 May 2026 09:27:55 GMT
• Title: Inverse Design for Conditional Distribution Matching
• Abstract summary: Conditional Distribution Matching (CDM) is a new inverse-design problem class in generative modeling.<n>We propose MLGD-F (Matching-Loss Guided Diffusion with a Fast inner sampler), a plug-and-play inference-time algorithm that combines a pretrained score-based diffusion model with a pretrained fast conditional sampler.<n>By leveraging single-step conditional sampling, MLGD-F enables tractable gradient computation, making the estimation of $mathcalP(Y mid X)$ both memory-efficient and computationally lightweight.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals are naturally distributional rather than pointwise, incorporating the inherent uncertainty of $Y$ and targeting a specific form for it, a task not addressed by standard inverse design. To address this issue we introduce Conditional Distribution Matching (CDM), a new inverse-design problem class in generative modeling: given a joint distribution $\mathcal{P}(X, Y)$ and a target distribution $\mathcal{G}(Y)$, find an input $x^*$ whose induced conditional distribution $\mathcal{P}(Y \mid X = x^*)$ matches $\mathcal{G}$. We formally define two variants: Conditional Distribution Matching Sampling (CDMS) and Conditional Distribution Matching Optimization (CDMO). To solve these problems, we propose MLGD-F (Matching-Loss Guided Diffusion with a Fast inner sampler), a plug-and-play inference-time algorithm that combines a pretrained score-based diffusion model with a pretrained fast conditional sampler, requiring no additional training or fine-tuning. By leveraging single-step conditional sampling, MLGD-F enables tractable gradient computation, making the estimation of $\mathcal{P}(Y \mid X)$ both memory-efficient and computationally lightweight. We validate MLGD-F on synthetic benchmarks, structured image transformations, and generative editing optimization, demonstrating reliable recovery of inputs whose conditional distributions match diverse user-specified targets, including discrete mixtures and continuous low-rank supports.

Related papers

• Provably adaptive sampling with uniform and remasking discrete diffusion models [9.180350432640912]
  We study a first-order sampler based on the leave-one-out denoiser for uniform and remasking processes.<n>Our main result establishes an adaptive sampling guarantee.<n> Numerical experiments on structured synthetic distributions illustrate the predicted dimension-adaptive behavior.
  arXiv  Detail & Related papers  (2026-08-24T17:54:51Z)
• Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions [13.856153548136826]
  Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution.<n>We study two DFM models on $mathbbZ_md = 0,ldots,m-1d$, sampled through time discretization.<n>We derive non-asymptotic bounds in Kullback--Leibler divergence for the early-stopped version of the target distribution.
  arXiv  Detail & Related papers  (2026-05-09T11:06:33Z)
• Spectral gap of Metropolis-within-Gibbs under log-concavity [1.4466802614938334]
  The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov Chain Monte Carlo method for sampling from high-dimensional distributions.<n>We study MwG with Random Walk Metropolis (RWM) updates, using proposal variances tuned to match the target's conditional variances.<n>The result shows that MwG can mix substantially faster with variance-adaptive proposals and that its mixing performance is just a constant factor worse than that of the exact Gibbs sampler.
  arXiv  Detail & Related papers  (2025-09-30T12:31:22Z)
• Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts [64.34482582690927]
  We provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models.<n>We propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality.
  arXiv  Detail & Related papers  (2025-03-04T17:46:51Z)
• Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative models [65.71506381302815]
  We propose amortize the cost of sampling from a posterior distribution of the form $p(mathbfxmidmathbfy) propto p_theta(mathbfx)$.<n>For many models and constraints, the posterior in noise space is smoother than in data space, making it more suitable for amortized inference.
  arXiv  Detail & Related papers  (2025-02-10T19:49:54Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Convergence Analysis of Probability Flow ODE for Score-based Generative Models [5.939858158928473]
  We study the convergence properties of deterministic samplers based on probability flow ODEs from both theoretical and numerical perspectives.<n>We prove the total variation between the target and the generated data distributions can be bounded above by $mathcalO(d3/4delta1/2)$ in the continuous time level.
  arXiv  Detail & Related papers  (2024-04-15T12:29:28Z)
• Distributed Extra-gradient with Optimal Complexity and Communication Guarantees [60.571030754252824]
  We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local dual vectors. Extra-gradient, which is a de facto algorithm for monotone VI problems, has not been designed to be communication-efficient. We propose a quantized generalized extra-gradient (Q-GenX), which is an unbiased and adaptive compression method tailored to solve VIs.
  arXiv  Detail & Related papers  (2023-08-17T21:15:04Z)
• Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyond [89.72693227960274]
  This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. To reduce the number of samples in each round from $m$ to 1, we cast GDRO as a two-player game, where one player conducts and the other executes an online algorithm for non-oblivious multi-armed bandits. In the second scenario, we propose to optimize the average top-$k$ risk instead of the maximum risk, thereby mitigating the impact of distributions.
  arXiv  Detail & Related papers  (2023-02-18T09:24:15Z)
• Convergence and Sample Complexity of SGD in GANs [15.25030172685628]
  We provide convergence guarantees on training Generative Adversarial Networks (GANs) via SGD. We consider learning a target distribution modeled by a 1-layer Generator network with a non-linear activation function. Our results apply to a broad class of non-linear activation functions $phi$, including ReLUs and is enabled by a connection with truncated statistics.
  arXiv  Detail & Related papers  (2020-12-01T18:50:38Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

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.