# Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAI

arXiv: https://arxiv.org/abs/2411.15265 · HTML: https://mlsanity.com/paper/2411.15265/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 65 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)

## Built on by (most cited first, 2 of 2)

- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [Training-Free Reward-Guided Image Editing via Trajectory Optimal Control](https://mlsanity.com/paper/2509.25845/) (2025)

## Abstract (arXiv)

Gradient-based methods are a prototypical family of explainability techniques, especially for image-based models. Nonetheless, they have several shortcomings in that they (1) require white-box access to models, (2) are vulnerable to adversarial attacks, and (3) produce attributions that lie off the image manifold, leading to explanations that are not actually faithful to the model and do not align well with human perception. To overcome these challenges, we introduce Derivative-Free Diffusion Manifold-Constrainted Gradients (FreeMCG), a novel method that serves as an improved basis for explainability of a given neural network than the traditional gradient. Specifically, by leveraging ensemble Kalman filters and diffusion models, we derive a derivative-free approximation of the model's gradient projected onto the data manifold, requiring access only to the model's outputs. We demonstrate the effectiveness of FreeMCG by applying it to both counterfactual generation and feature attribution, which have traditionally been treated as distinct tasks. Through comprehensive evaluation on both tasks, counterfactual explanation and feature attribution, we show that our method yields state-of-the-art results while preserving the essential properties expected of XAI tools.