# Diffusion models recover accurate mixture weights despite score function insensitivity arXiv: https://arxiv.org/abs/2607.15485 ยท HTML: https://mlsanity.com/paper/2607.15485/ ## Key facts - Cited by 3 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 36 of its 63 references that are in the map. - First posted on arXiv 16 Jul 2026. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 36) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019) - [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022) - [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020) - [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018) - [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020) - [Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models](https://mlsanity.com/paper/2306.04675/) (2023) - [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021) - [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022) - [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021) - [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024) - [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023) - [Statistical Efficiency of Score Matching: The View from Isoperimetry](https://mlsanity.com/paper/2210.00726/) (2022) - [Learning Mixtures of Gaussians Using the DDPM Objective](https://mlsanity.com/paper/2307.01178/) (2023) - [Learning general Gaussian mixtures with efficient score matching](https://mlsanity.com/paper/2404.18893/) (2024) - [Learning Mixtures of Gaussians Using Diffusion Models](https://mlsanity.com/paper/2404.18869/) (2024) - [Improved Noise Schedule for Diffusion Training](https://mlsanity.com/paper/2407.03297/) (2024) - [Your diffusion model secretly knows the dimension of the data manifold](https://mlsanity.com/paper/2212.12611/) (2022) - [Beyond Log-concavity: Provable Guarantees for Sampling Multi-modal Distributions using Simulated Tempering Langevin Monte Carlo](https://mlsanity.com/paper/1710.02736/) (2017) - [Machine learning emulation of precipitation from km-scale UK regional climate simulations using a diffusion model](https://mlsanity.com/paper/2407.14158/) (2024) - [Position: All Current Generative Fidelity and Diversity Metrics are Flawed](https://mlsanity.com/paper/2505.22450/) (2025) - [A Review on Generative AI Models for Synthetic Medical Text, Time Series, and Longitudinal Data](https://mlsanity.com/paper/2411.12274/) (2024) - [Fit Like You Sample: Sample-Efficient Generalized Score Matching from Fast Mixing Diffusions](https://mlsanity.com/paper/2306.09332/) (2023) - [Soft Mixture Denoising: Beyond the Expressive Bottleneck of Diffusion Models](https://mlsanity.com/paper/2309.14068/) (2023) ## Built on by (most cited first, 3 of 3) - [Recovering Weighted Tangent Geometry from a Single-Scale Score Field](https://mlsanity.com/paper/2608.22334/) (2026) - [Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression](https://mlsanity.com/paper/2609.05688/) (2026) - [Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers](https://mlsanity.com/paper/2609.26272/) (2026) ## Abstract (arXiv) Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative mode amplitudes, which can be interpreted as mixture weights. We resolve this apparent paradox by relating the diffusion score matching (DSM) loss to the error in estimating mixture weights from generated samples. We show that, even when the target score is insensitive to mixture weights, generated samples can recover the weights accurately if the scores at intermediate noise levels are informative about the weights. Accordingly, we define the diffusion score sensitivity index (DSSI) as the variation in the DSM loss relative to changes in a parameter. We then show that the DSSI governs the accuracy with which the parameter of the target distribution can be estimated from generated samples. For Gaussian mixtures in arbitrary dimensions, we prove that the mixture weight estimation errors are on the same order as the DSM loss under mild conditions. Empirically, we show the emergence of sensitivity during the noising process of benchmark data distributions under typical noise schedules, and that these sensitivity values predict how well a well-trained model recovers mixture weights. Furthermore, we show that the choice of noise schedule can reduce diffusion sensitivity, leading to mode amplification. Although we focus on mixture weights, the proposed sensitivity framework governs the recovery of any qualitative parameter of the target distribution.