# Is Your Conditional Diffusion Model Actually Denoising?

arXiv: https://arxiv.org/abs/2512.18736 · HTML: https://mlsanity.com/paper/2512.18736/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Placed in

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

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

- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent](https://mlsanity.com/paper/2302.09057/) (2023)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [Closed-Form Diffusion Models](https://mlsanity.com/paper/2310.12395/) (2023)
- [The Superposition of Diffusion Models Using the Ito Density Estimator](https://mlsanity.com/paper/2412.17762/) (2024)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [Interpreting and Improving Diffusion Models from an Optimization Perspective](https://mlsanity.com/paper/2306.04848/) (2023)

## Built on by (most cited first, 1 of 1)

- [Spectral Collapse in Diffusion Inversion](https://mlsanity.com/paper/2602.13303/) (2026)

## Abstract (arXiv)

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that when these models are queried conditionally, their generations consistently deviate from the idealized "denoising" process upon which diffusion models are formulated, inducing disagreement between popular sampling algorithms (e.g. DDPM, DDIM). We introduce Schedule Deviation, a rigorous measure which captures the rate of deviation from a standard denoising process, and provide a methodology to compute it. Crucially, we demonstrate that the deviation from an idealized denoising process occurs irrespective of the model capacity or amount of training data. We posit that this phenomenon occurs due to the difficulty of bridging distinct denoising flows across different parts of the conditioning space and show theoretically how such a phenomenon can arise through an inductive bias towards smoothness.