# Latent Structure Emergence in Diffusion Models via Confidence-Based Filtering

arXiv: https://arxiv.org/abs/2602.06155 · HTML: https://mlsanity.com/paper/2602.06155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence](https://mlsanity.com/paper/2305.14334/) (2023)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization](https://mlsanity.com/paper/2404.04650/) (2024)
- [Diffusion Model as Representation Learner](https://mlsanity.com/paper/2308.10916/) (2023)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Generating images of rare concepts using pre-trained diffusion models](https://mlsanity.com/paper/2304.14530/) (2023)
- [Readout Guidance: Learning Control from Diffusion Features](https://mlsanity.com/paper/2312.02150/) (2023)
- [Good Seed Makes a Good Crop: Discovering Secret Seeds in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2405.14828/) (2024)
- [CleanDIFT: Diffusion Features without Noise](https://mlsanity.com/paper/2412.03439/) (2024)
- [textitRevelio: Interpreting and leveraging semantic information in diffusion models](https://mlsanity.com/paper/2411.16725/) (2024)
- [Measuring Semantic Information Production in Generative Diffusion Models](https://mlsanity.com/paper/2506.10433/) (2025)
- [Latent Abstractions in Generative Diffusion Models](https://mlsanity.com/paper/2410.03368/) (2024)

## Abstract (arXiv)

Diffusion models generate samples through a sequence of learned denoising steps, and recent work has studied how semantic structure appears along this sampling process. We study this question in deterministic samplers by measuring semantic accessibility: how much information about a final semantic property, such as an image class label or attribute, can be extracted from the seed and intermediate states along the trajectory that produces the sample. Using DDIM sampling, for which each initial noise seed determines a unique trajectory and final image, we train separate classifiers (probes) at several points along the trajectory to predict a semantic property of the final image. We measure how well such a property can be predicted from the state at a given point using top-1 accuracy and normalized mutual information. Across MNIST, Fashion-MNIST, CIFAR-10, and CelebA, class labels and image attributes can be predicted above chance from the initial noise seed, and along DDIM trajectories, this accessibility exceeds matched-noise forward baselines. We find that semantic accessibility is substantially higher along the trajectories whose final images are classified with high confidence than along those classified with low confidence. These measurements provide a quantitative view of when semantic properties can be recovered during deterministic generation.