# Implicit Diffusion: Efficient Optimization through Stochastic Sampling

arXiv: https://arxiv.org/abs/2402.05468 · HTML: https://mlsanity.com/paper/2402.05468/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 99 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 30 of 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Aligning Text-to-Image Models using Human Feedback](https://mlsanity.com/paper/2302.12192/) (2023)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Human Preference Score: Better Aligning Text-to-Image Models with Human Preference](https://mlsanity.com/paper/2303.14420/) (2023)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)

## Built on by (most cited first, 24 of 24)

- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024)
- [Fine-Tuning Discrete Diffusion Models with Policy Gradient Methods](https://mlsanity.com/paper/2502.01384/) (2025)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [Functional Bilevel Optimization for Machine Learning](https://mlsanity.com/paper/2403.20233/) (2024)
- [Attention layers provably solve single-location regression](https://mlsanity.com/paper/2410.01537/) (2024)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics](https://mlsanity.com/paper/2410.09697/) (2024)
- [AdjointDEIS: Efficient Gradients for Diffusion Models](https://mlsanity.com/paper/2405.15020/) (2024)
- [Direct Distributional Optimization for Provable Alignment of Diffusion Models](https://mlsanity.com/paper/2502.02954/) (2025)
- [A First-order Generative Bilevel Optimization Framework for Diffusion Models](https://mlsanity.com/paper/2502.08808/) (2025)
- [DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows](https://mlsanity.com/paper/2503.01140/) (2025)
- [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025)
- [Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories](https://mlsanity.com/paper/2511.07368/) (2025)
- [Greed is Good: A Unifying Perspective on Guided Generation](https://mlsanity.com/paper/2502.08006/) (2025)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)
- [Efficient Stochastic Optimisation via Sequential Monte Carlo](https://mlsanity.com/paper/2601.22003/) (2026)
- [Diffusion Fine-tuning with Rewarded Moment Matching Distillation](https://mlsanity.com/paper/2606.30414/) (2026)
- [Trading Devil Final: Backdoor attack via Stock market and Bayesian Optimization](https://mlsanity.com/paper/2407.14573/) (2024)
- [Particle-based Generalised Stochastic Optimisation](https://mlsanity.com/paper/2608.02844/) (2026)
- [Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Models](https://mlsanity.com/paper/2609.39091/) (2026)
- [Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models](https://mlsanity.com/paper/2610.16851/) (2026)
- [Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost](https://mlsanity.com/paper/2610.20035/) (2026)

## Abstract (arXiv)

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness. We apply it to training energy-based models and finetuning denoising diffusions.