The paper introduces a new algorithm called Implicit Diffusion, which optimizes distributions defined by parameterized stochastic diffusions. This approach allows for modifying the outcome distribution of sampling processes by optimizing their parameters. The authors present a general framework for first-order optimization of these processes, which performs both optimization and sampling in a single loop. This method is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the perspective of sampling as optimization over the space of probability distributions. The paper provides theoretical guarantees on the performance of the method and demonstrates its effectiveness through experimental results, including applications to training energy-based models and finetuning denoising diffusions. The main contributions include a general framework for parameterized sampling algorithms, the introduction of Implicit Diffusion optimization, and theoretical and experimental validation of its performance.The paper introduces a new algorithm called Implicit Diffusion, which optimizes distributions defined by parameterized stochastic diffusions. This approach allows for modifying the outcome distribution of sampling processes by optimizing their parameters. The authors present a general framework for first-order optimization of these processes, which performs both optimization and sampling in a single loop. This method is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the perspective of sampling as optimization over the space of probability distributions. The paper provides theoretical guarantees on the performance of the method and demonstrates its effectiveness through experimental results, including applications to training energy-based models and finetuning denoising diffusions. The main contributions include a general framework for parameterized sampling algorithms, the introduction of Implicit Diffusion optimization, and theoretical and experimental validation of its performance.