# deepinv.sampling This module contains various posterior sampling algorithms, including diffusion-based methods and MCMC methods. Please refer to the [user guide](https://deepinv.org/user_guide/reconstruction/sampling.html.md#sampling) for more details. ## Diffusion models with Stochastic Differential Equations for Image Generation and Posterior Sampling **User Guide:** refer to [Diffusion models](https://deepinv.org/user_guide/reconstruction/sampling.html.md#diffusion) for more information. | [`deepinv.sampling.BaseSDE`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSDE.html.md#deepinv.sampling.BaseSDE) | Base class for Stochastic Differential Equation (SDE): | |--------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | [`deepinv.sampling.DiffusionSDE`](https://deepinv.org/api/stubs/deepinv.sampling.DiffusionSDE.html.md#deepinv.sampling.DiffusionSDE) | Define the Reverse-time Diffusion Stochastic Differential Equation. | | [`deepinv.sampling.EDMDiffusionSDE`](https://deepinv.org/api/stubs/deepinv.sampling.EDMDiffusionSDE.html.md#deepinv.sampling.EDMDiffusionSDE) | Generative diffusion Stochastic Differential Equation. | | [`deepinv.sampling.SongDiffusionSDE`](https://deepinv.org/api/stubs/deepinv.sampling.SongDiffusionSDE.html.md#deepinv.sampling.SongDiffusionSDE) | Generative diffusion Stochastic Differential Equation. | | [`deepinv.sampling.FlowMatching`](https://deepinv.org/api/stubs/deepinv.sampling.FlowMatching.html.md#deepinv.sampling.FlowMatching) | Generative Flow Matching process. | | [`deepinv.sampling.VarianceExplodingDiffusion`](https://deepinv.org/api/stubs/deepinv.sampling.VarianceExplodingDiffusion.html.md#deepinv.sampling.VarianceExplodingDiffusion) | | | [`deepinv.sampling.VariancePreservingDiffusion`](https://deepinv.org/api/stubs/deepinv.sampling.VariancePreservingDiffusion.html.md#deepinv.sampling.VariancePreservingDiffusion) | Variance-Preserving Stochastic Differential Equation (VP-SDE). | | [`deepinv.sampling.PosteriorDiffusion`](https://deepinv.org/api/stubs/deepinv.sampling.PosteriorDiffusion.html.md#deepinv.sampling.PosteriorDiffusion) | Posterior distribution sampling for inverse problems using diffusion models by Reverse-time Stochastic Differential Equation (SDE). | | [`deepinv.sampling.NoisyDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.NoisyDataFidelity.html.md#deepinv.sampling.NoisyDataFidelity) | Data fidelity term for noisy input data $- \log p(y|x + \sigma(t) \omega)$ with $\omega\sim\mathcal{N}(0,\mathrm{I})$. | | [`deepinv.sampling.ALDDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.ALDDataFidelity.html.md#deepinv.sampling.ALDDataFidelity) | Score-based annealed Langevin dynamics (Score-ALD) data-fidelity term. | | [`deepinv.sampling.ScoreSDEDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.ScoreSDEDataFidelity.html.md#deepinv.sampling.ScoreSDEDataFidelity) | Score-SDE data-fidelity term. | | [`deepinv.sampling.ILVRDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.ILVRDataFidelity.html.md#deepinv.sampling.ILVRDataFidelity) | Iterative Latent Variable Refinement (ILVR) data-fidelity term. | | [`deepinv.sampling.DPSDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.DPSDataFidelity.html.md#deepinv.sampling.DPSDataFidelity) | Diffusion posterior sampling data-fidelity term. | | [`deepinv.sampling.PiGDMDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.PiGDMDataFidelity.html.md#deepinv.sampling.PiGDMDataFidelity) | Pseudoinverse-guided diffusion model (PiGDM) data-fidelity term. | | [`deepinv.sampling.MomentMatchingDataFidelity`](https://deepinv.org/api/stubs/deepinv.sampling.MomentMatchingDataFidelity.html.md#deepinv.sampling.MomentMatchingDataFidelity) | Moment-matching data-fidelity term for diffusion posterior sampling. | | [`deepinv.sampling.BaseSDESolver`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSDESolver.html.md#deepinv.sampling.BaseSDESolver) | Base class for solving Stochastic Differential Equations (SDEs) from [`deepinv.sampling.BaseSDE`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSDE.html.md#deepinv.sampling.BaseSDE) of the form: | | [`deepinv.sampling.EulerSolver`](https://deepinv.org/api/stubs/deepinv.sampling.EulerSolver.html.md#deepinv.sampling.EulerSolver) | Euler-Maruyama solver for SDEs. | | [`deepinv.sampling.HeunSolver`](https://deepinv.org/api/stubs/deepinv.sampling.HeunSolver.html.md#deepinv.sampling.HeunSolver) | Heun solver for SDEs. | | [`deepinv.sampling.AncestralSolver`](https://deepinv.org/api/stubs/deepinv.sampling.AncestralSolver.html.md#deepinv.sampling.AncestralSolver) | Ancestral solver for reverse-time diffusion SDEs, generalizing the DDPM and DDIM samplers. | | [`deepinv.sampling.DDPMSolver`](https://deepinv.org/api/stubs/deepinv.sampling.DDPMSolver.html.md#deepinv.sampling.DDPMSolver) | DDPM solver for reverse-time diffusion SDEs. | | [`deepinv.sampling.DDIMSolver`](https://deepinv.org/api/stubs/deepinv.sampling.DDIMSolver.html.md#deepinv.sampling.DDIMSolver) | DDIM solver for reverse-time diffusion SDEs. | | [`deepinv.sampling.SDEOutput`](https://deepinv.org/api/stubs/deepinv.sampling.SDEOutput.html.md#deepinv.sampling.SDEOutput) | A container for storing the output of an SDE solver, that behaves like a `dict` but allows access with the attribute syntax. | ## Custom diffusion posterior samplers **User Guide:** refer to [Popular posterior samplers](https://deepinv.org/user_guide/reconstruction/sampling.html.md#diffusion-custom) for more information. | [`deepinv.sampling.DDRM`](https://deepinv.org/api/stubs/deepinv.sampling.DDRM.html.md#deepinv.sampling.DDRM) | Denoising Diffusion Restoration Models (DDRM). | |----------------------------------------------------------------------------------------------------------------------|------------------------------------------------------| | [`deepinv.sampling.DiffPIR`](https://deepinv.org/api/stubs/deepinv.sampling.DiffPIR.html.md#deepinv.sampling.DiffPIR) | Diffusion PnP Image Restoration (DiffPIR). | | [`deepinv.sampling.DPS`](https://deepinv.org/api/stubs/deepinv.sampling.DPS.html.md#deepinv.sampling.DPS) | Diffusion Posterior Sampling (DPS). | | [`deepinv.sampling.DiffusionSampler`](https://deepinv.org/api/stubs/deepinv.sampling.DiffusionSampler.html.md#deepinv.sampling.DiffusionSampler) | Turns a diffusion method into a Monte Carlo sampler. | ## Base Class **User Guide:** refer to [Diffusion and MCMC Algorithms](https://deepinv.org/user_guide/reconstruction/sampling.html.md#sampling) for more information. | [`deepinv.sampling.sampling_builder`](https://deepinv.org/api/stubs/deepinv.sampling.sampling_builder.html.md#deepinv.sampling.sampling_builder) | Helper function for building an instance of the [`deepinv.sampling.BaseSampling`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSampling.html.md#deepinv.sampling.BaseSampling) class. | |------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------| | [`deepinv.sampling.BaseSampling`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSampling.html.md#deepinv.sampling.BaseSampling) | Base class for Monte Carlo sampling. | |----------------------------------------------------------------------------------------------------------------|----------------------------------------| ## Markov Chain Monte Carlo Langevin **User Guide:** refer to [Markov Chain Monte Carlo](https://deepinv.org/user_guide/reconstruction/sampling.html.md#mcmc) for more information. | [`deepinv.sampling.ULA`](https://deepinv.org/api/stubs/deepinv.sampling.ULA.html.md#deepinv.sampling.ULA) | Projected Plug-and-Play Unadjusted Langevin Algorithm. | |--------------------------------------------------------------------------------------------------|----------------------------------------------------------| | [`deepinv.sampling.SKRock`](https://deepinv.org/api/stubs/deepinv.sampling.SKRock.html.md#deepinv.sampling.SKRock) | Plug-and-Play SKROCK algorithm. | ## Iterators | [`deepinv.sampling.SamplingIterator`](https://deepinv.org/api/stubs/deepinv.sampling.SamplingIterator.html.md#deepinv.sampling.SamplingIterator) | Base class for sampling iterators. | |------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | [`deepinv.sampling.SKRockIterator`](https://deepinv.org/api/stubs/deepinv.sampling.SKRockIterator.html.md#deepinv.sampling.SKRockIterator) | Single iteration of the SK-ROCK (Stabilized Runge-Kutta-Chebyshev) Algorithm. | | [`deepinv.sampling.ULAIterator`](https://deepinv.org/api/stubs/deepinv.sampling.ULAIterator.html.md#deepinv.sampling.ULAIterator) | Projected Plug-and-Play Unadjusted Langevin Algorithm. | | [`deepinv.sampling.DiffusionIterator`](https://deepinv.org/api/stubs/deepinv.sampling.DiffusionIterator.html.md#deepinv.sampling.DiffusionIterator) | Helper class used by [`deepinv.sampling.DiffusionSampler`](https://deepinv.org/api/stubs/deepinv.sampling.DiffusionSampler.html.md#deepinv.sampling.DiffusionSampler) to interface diffusion models with the [`deepinv.sampling.BaseSampling`](https://deepinv.org/api/stubs/deepinv.sampling.BaseSampling.html.md#deepinv.sampling.BaseSampling) framework. |