Information-Calibrated Quantum Diffusion: Aligning Forward Noise with Reverse Recoverability

• URL: http://arxiv.org/abs/2608.14083v2
• Date: Tue, 18 Aug 2026 05:56:43 GMT
• Title: Information-Calibrated Quantum Diffusion: Aligning Forward Noise with Reverse Recoverability
• Abstract summary: We introduce the classical--quantum information decrement $_t=I(X:Q_t-1)-I(X:Q_t) as an intrinsic diffusion coordinate.<n>Along depolarization, equalizing $_t$ yields the unique minimax discretization of the forward information loss.
• Score: 10.481986290704821
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum diffusion models typically parameterize forward corruption by raw channel strength, even though this parameter does not directly quantify how much ensemble information is erased or how difficult the corresponding reverse problem is. We introduce the classical--quantum information decrement $Δ_t=I(X{:}Q_{t-1})-I(X{:}Q_t)$ as an intrinsic diffusion coordinate that links forward noise allocation to reverse recoverability. Along depolarization, equalizing $Δ_t$ yields the unique minimax discretization of the forward information loss, while universal recoverability gives the same quantity an operational interpretation as a physically attainable local recovery budget. We further show that such local calibration is not sufficient for stochastic generation: models can satisfy the same recovery criterion while producing substantially different state distributions. This motivates a stochastic learner that combines information-calibrated recovery constraints with distribution matching. We establish finite-sample calibration and compositional trace-Wasserstein control for the resulting learner. Controlled quantum experiments validate the predicted information--recovery alignment, show that the recovery constraints improve local inversion, and confirm the complementary role of distribution matching in endpoint generation. The resulting framework also achieves stronger endpoint trace-Wasserstein performance than an official QuDDPM implementation with fewer trainable parameters. Overall, our work provides a unified information-theoretic principle for designing forward schedules, calibrating reverse steps, and separating physical recovery from generative coverage in quantum diffusion.

Related papers

• RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation [2.589687124983865]
  Multi-time series imputation aims to recover missing values in temporal data composed of multiple variables.<n>This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems.<n>Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising.
  arXiv  Detail & Related papers  (2026-09-10T14:53:38Z)
• Scale-Consistent Posterior Dynamics for Diffusion Inverse Problems [16.685352002333225]
  Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose likelihood component is generally intractable.<n>We show that a noise-conditioned path whose targets approach the clean posterior produces a continuous surrogate SDE.<n>Experiments on FFHQ and ImageNet with 100 score evaluations demonstrate competitive reconstruction fidelity for superresolution and deblurring.
  arXiv  Detail & Related papers  (2026-08-15T09:38:41Z)
• Simplex Relaxation for Discrete Diffusion [58.33696160279345]
  We introduce Simplax, an exact Dirichlet--categorical augmentation that couples each corrupted categorical state with an auxiliary simplex-valued variable.<n>Simplax improves the generative perplexity--entropy tradeoff on unconditional OpenWebText generation.
  arXiv  Detail & Related papers  (2026-08-11T07:58:17Z)
• Quantum Error Mitigation with Diffusion-Like Models [0.1957338076370071]
  Coupling between a quantum system and its environment causes decoherence by transferring information from the system to environmental degrees of freedom.<n>We propose an AI-assisted error-mitigation framework for quantum diffusion processes generated by sequential local weak measurements.<n>The framework provides a hybrid classical-quantum approach for approximating non-unitary dynamics and mitigating coherence loss.
  arXiv  Detail & Related papers  (2026-08-05T20:05:50Z)
• Convex-Hull-Neighborhood Smooth Dual Generalization: Controlling Local Correction Propagation in Offline RL [7.803284875836737]
  bootstrapping can amplify estimation errors in offline reinforcement learning.<n>We propose Convex Hull Neighborhood Smooth Dual Generalization, which expresses the Bellman backup as an in-sample value target plus a CHN-local correction.<n> Experiments on Gym-MuJoCo and AntMaze show strong aggregate performance and stable value estimation.
  arXiv  Detail & Related papers  (2026-08-04T04:30:02Z)
• Tight Information Complexity of the Coin Problem in the Broadcast Model [0.21485350418225238]
  We study distributed testing of $mathrmBer()$ versus $mathrmBer()$ in the broadcast, or shared-blackboard, model.<n>For protocols with constant advantage, we characterise up to universal constant factors the information complexity under either hypothesis for every pair $$.
  arXiv  Detail & Related papers  (2026-08-03T18:21:26Z)
• Active Quantum Kernel Acquisition for Gaussian Process Regression [30.032230630492155]
  Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries can reduce the shot budget required to reach a target accuracy.<n>We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification.<n>We derive three closed-form pair-level sensitivities predictive coupling $|_i_j|$, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum
  arXiv  Detail & Related papers  (2026-06-27T09:40:20Z)
• One-Bit Clustering for Two Component Sub-Gaussian Mixture Models [17.177800879292963]
  We propose the first one-bit clustering method for two-component sub-Gaussian mixture models.<n>The method uses only one bit per entry of each sample obtained via a dithered quantizer.
  arXiv  Detail & Related papers  (2026-06-20T04:18:08Z)
• Clipping Bottleneck: Stabilizing RLVR via Stochastic Recovery of Near-Boundary Signals [83.0127582612634]
  Near-boundary Rescue (NSR) is a minimal, plug-and-play modification that retains out-of-bound tokens to recover lost signals.<n>NSR substantially improves training stability and delivers consistent gains over strong baselines such as DAPO and GSPO.
  arXiv  Detail & Related papers  (2026-05-21T16:45:31Z)
• Learning from Emptiness: De-biasing Listwise Rerankers with Content-Agnostic Probability Calibration [76.08899010904652]
  CapCal is a training-free framework that mechanically decouples positional bias from ranking decisions.<n>It achieves superior performance among training-free methods while preserving single-pass efficiency.
  arXiv  Detail & Related papers  (2026-04-11T10:47:22Z)
• Reinforcement Learning from Multi-Source Imperfect Preferences: Best-of-Both-Regimes Regret [71.69884486156359]
  We study episodic RL from emphmulti-source imperfect preferences through a cumulative imperfection budget.<n>We propose a unified algorithm with regret $tildeO(sqrtK/M+)$, which exhibits a best-of-both-regimes behavior.
  arXiv  Detail & Related papers  (2026-03-20T19:34:53Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• Analysis of Hessian Scaling for Local and Global Costs in Variational Quantum Algorithm [0.42970700836450487]
  We quantify the entrywise resolvability of the Hessian for Variational Quantum Algorithms.<n>We show two distinct scaling regimes that govern the sample complexity required to resolve Hessian entries against shot noise.
  arXiv  Detail & Related papers  (2026-01-31T15:49:23Z)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Entropy-Reservoir Bregman Projection: An Information-Geometric Unification of Model Collapse [3.533187668612022]
  We present EntropyReser Bregman Projection- ERBP, an information-geometric framework that unifies these phenomena.<n>Our theory yields a necessary condition for collapse, (ii) a sufficient condition that guarantees a non-language entropy floor, and (iii) closed-form rates that depend on sample size.
  arXiv  Detail & Related papers  (2025-12-16T19:50:03Z)
• QuantSparse: Comprehensively Compressing Video Diffusion Transformer with Model Quantization and Attention Sparsification [67.15451442018258]
  Diffusion transformers exhibit remarkable video generation capability, yet their prohibitive computational and memory costs hinder practical deployment.<n>Model quantization and attention sparsification are two promising directions for compression, but each alone suffers severe performance degradation under aggressive compression.<n>We propose textbfQuantSparse, a unified framework that integrates model quantization with attention sparsification.
  arXiv  Detail & Related papers  (2025-09-28T06:49:44Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Bayesian Renormalization [68.8204255655161]
  We present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference. The main insight of Bayesian Renormalization is that the Fisher metric defines a correlation length that plays the role of an emergent RG scale. We provide insight into how the Bayesian Renormalization scheme relates to existing methods for data compression and data generation.
  arXiv  Detail & Related papers  (2023-05-17T18:00:28Z)
• Permutation Compressors for Provably Faster Distributed Nonconvex Optimization [68.8204255655161]
  We show that the MARINA method of Gorbunov et al (2021) can be considered as a state-of-the-art method in terms of theoretical communication complexity. Theory of MARINA to support the theory of potentially em correlated compressors, extends to the method beyond the classical independent compressors setting.
  arXiv  Detail & Related papers  (2021-10-07T09:38:15Z)

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.