diff --git a/.github/workflows/docs-link-check.yml b/.github/workflows/docs-link-check.yml
new file mode 100644
index 000000000..bf454f17c
--- /dev/null
+++ b/.github/workflows/docs-link-check.yml
@@ -0,0 +1,38 @@
+name: Docs Link Check
+
+# Validates the hard-coded URLs in llms.txt and AGENTS.md, which are not covered by
+# any other CI. Runs monthly rather than per-PR so transient or rate-limited external
+# responses don't block contributors.
+
+on:
+  schedule:
+    - cron: '0 6 1 * *'  # 06:00 UTC on the 1st of each month
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+defaults:
+  run:
+    shell: bash
+
+jobs:
+  link-check:
+    name: Check documentation links
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
+        with:
+          lfs: false
+          persist-credentials: false
+
+      - name: Check links with lychee
+        uses: lycheeverse/lychee-action@e7477775783ea5526144ba13e8db5eec57747ce8 # v2.9.0
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}  # authenticate github.com links (avoid 60/hr rate limit)
+        with:
+          args: >-
+            --no-progress --verbose
+            docs/llms.txt AGENTS.md
+          fail: true
diff --git a/AGENTS.md b/AGENTS.md
new file mode 100644
index 000000000..089a9a98a
--- /dev/null
+++ b/AGENTS.md
@@ -0,0 +1,55 @@
+# AGENTS.md — sbi
+
+Shared guidance for coding agents working in this repository.
+
+## Setup
+
+```bash
+uv venv --python 3.12
+uv pip install -e ".[dev]"
+```
+
+Run validation commands through `uv run`; activating the virtual environment is
+optional. See `docs/contributing.md` for the full development workflow and
+`pyproject.toml` for the authoritative tool configuration.
+
+## Validation
+
+Start with checks targeted to the files and behavior you changed, then broaden as
+appropriate:
+
+```bash
+uv run pytest tests/path_to_relevant_test.py
+uv run pytest -n auto -m "not slow and not gpu"
+uv run ruff check <changed Python paths>
+uv run ruff format --check <changed Python paths>
+uv run pyright sbi
+uv run pre-commit run --files <changed files>
+```
+
+Tests live in `*_test.py` files. Available markers include `slow`, `gpu`, `mcmc`, and
+`benchmark`; their definitions are in `pyproject.toml`.
+
+## Code conventions
+
+- Use Google-style docstrings.
+- Put shared public type aliases in `sbi/sbi_types.py`.
+- Keep string identifiers for estimators lowercase (for example, `"maf"`, `"nsf"`,
+  and `"mdn"`).
+- Add or update tests when behavior changes.
+- Preserve unrelated local changes. If a checkout is already in use, work in a
+  separate Git worktree.
+
+## Code map
+
+Inspect the current code rather than relying on a duplicated class inventory:
+
+- `sbi/inference/__init__.py` — public inference methods
+- `sbi/inference/trainers/` — training workflows
+- `sbi/inference/posteriors/` — posterior implementations
+- `sbi/inference/potentials/` — estimator-to-sampler bridges
+- `sbi/neural_nets/estimators/` — estimator contracts and implementations
+- `sbi/samplers/` — sampling backends
+
+The documentation is built from `docs/`. Its curated `docs/llms.txt` index is served
+at `https://sbi.readthedocs.io/en/latest/llms.txt` for tools that support it.
diff --git a/CLAUDE.md b/CLAUDE.md
new file mode 100644
index 000000000..248e45d22
--- /dev/null
+++ b/CLAUDE.md
@@ -0,0 +1,6 @@
+# CLAUDE.md
+
+This repository's instructions for AI coding agents live in `AGENTS.md` (shared across
+all tools). Claude Code imports them here:
+
+@AGENTS.md
diff --git a/docs/conf.py b/docs/conf.py
index 8ca740457..11166247a 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -55,6 +55,9 @@
 # This pattern also affects html_static_path and html_extra_path.
 exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']
 
+# Serve llms.txt at the docs URL root for AI agent discoverability.
+html_extra_path = ['llms.txt']
+
 # Myst-NB
 myst_enable_extensions = [
     "dollarmath",
diff --git a/docs/contributor_guide.rst b/docs/contributor_guide.rst
index 3939d86bd..c90d438cd 100644
--- a/docs/contributor_guide.rst
+++ b/docs/contributor_guide.rst
@@ -5,7 +5,8 @@ Developer notes
 
 `sbi` welcomes contributions from the community.
 These are guides to get set up as a developer, as well as
-developer-focused resources.
+developer-focused resources. For a list of current and former project
+maintainers, see the :doc:`credits page <credits>`.
 
 
 .. toctree::
diff --git a/docs/credits.md b/docs/credits.md
index 4cd52d163..fea10cd09 100644
--- a/docs/credits.md
+++ b/docs/credits.md
@@ -6,6 +6,22 @@
 played a significant role in shaping `sbi`. Their valuable input, suggestions, and
 direct contributions to the codebase have been instrumental in the development of `sbi`.
 
+## Maintainers
+
+`sbi` is maintained by the following people. Current maintainers are
+
+- [Jan Teusen (né Boelts)](https://github.com/janfb)
+- [Manuel Gloeckler](https://github.com/manuelgloeckler)
+- [Daniel Gedon](https://github.com/dgedon)
+- [Stefan Wahl](https://github.com/StefanWahl)
+
+Former maintainers are
+
+- [Michael Deistler](https://github.com/michaeldeistler)
+- [Guy Moss](https://github.com/gmoss13)
+- [Jan-Matthis Lückmann](https://github.com/jan-matthis)
+- [Alvaro Tejero-Cantero](https://github.com/alvorithm)
+
 ## License
 
 `sbi` is licensed under the [Apache License
diff --git a/docs/llms.txt b/docs/llms.txt
new file mode 100644
index 000000000..2405f2a5c
--- /dev/null
+++ b/docs/llms.txt
@@ -0,0 +1,72 @@
+# sbi: Simulation-Based Inference
+
+> sbi is a PyTorch-based Python package for simulation-based inference (SBI).
+> It estimates full Bayesian posterior distributions over simulator parameters
+> from observed data, without requiring access to the simulator's likelihood
+> function. Methods include Neural Posterior Estimation (NPE), Neural Likelihood
+> Estimation (NLE), Neural Ratio Estimation (NRE), and flow/score matching (FMPE, NPSE).
+
+sbi provides both a simple one-line interface (`sbi.inference.infer`) and a
+flexible class-based interface (`NPE`, `NLE`, `NRE`, `FMPE`). The typical
+workflow is: define a prior and simulator, generate simulations, train a neural
+density estimator, build a posterior, and validate with diagnostics (SBC,
+expected coverage, TARP, L-C2ST).
+
+## Tutorials
+
+- [Getting Started](https://sbi.readthedocs.io/en/latest/tutorials/00_getting_started.html): Minimal NPE example from prior to posterior
+- [Bayesian Workflow](https://sbi.readthedocs.io/en/latest/tutorials/01_Bayesian_workflow.html): Full workflow with diagnostics and analysis
+- [Implemented Methods](https://sbi.readthedocs.io/en/latest/tutorials/16_implemented_methods.html): All NPE, NLE, NRE, FMPE variants with code
+- [Vector Field Methods](https://sbi.readthedocs.io/en/latest/advanced_tutorials/19_vector_field_methods.html): FMPE and NPSE — flow matching and score matching for SBI
+
+## How-To Guides
+
+- [Custom Priors](https://sbi.readthedocs.io/en/latest/how_to_guide/00_custom_prior.html): MultipleIndependent, process_prior, non-torch priors
+- [Summary Statistics](https://sbi.readthedocs.io/en/latest/how_to_guide/01_crafting_summary_statistics.html): Hand-crafted features for high-dim data
+- [Multi-Round Inference](https://sbi.readthedocs.io/en/latest/how_to_guide/02_multiround_inference.html): Sequential methods (SNPE, SNLE, SNRE)
+- [Density Estimators](https://sbi.readthedocs.io/en/latest/how_to_guide/03_density_estimators.html): Choosing and configuring neural networks
+- [Embedding Networks](https://sbi.readthedocs.io/en/latest/how_to_guide/04_embedding_networks.html): FCEmbedding, CNNEmbedding, custom nn.Module
+- [Choosing Inference Method](https://sbi.readthedocs.io/en/latest/how_to_guide/06_choosing_inference_method.html): NPE vs NLE vs NRE decision guide
+- [Sampler Interface](https://sbi.readthedocs.io/en/latest/how_to_guide/09_sampler_interface.html): MCMC, VI, rejection for NLE/NRE posteriors
+- [i.i.d. Observations](https://sbi.readthedocs.io/en/latest/how_to_guide/11_iid_sampling_with_nle_or_nre.html): Multiple observations with NLE/NRE
+- [Hyperparameter Tuning](https://sbi.readthedocs.io/en/latest/how_to_guide/21_hyperparameter_tuning.html): Optuna integration for architecture search
+- [Abstraction Levels](https://sbi.readthedocs.io/en/latest/how_to_guide/24_abstraction_levels.html): Four levels of control over the density estimator (Trainer classes to custom `nn.Module`), plus sampling-control levels for NLE
+- [FMPE and NPSE Recommendations](https://sbi.readthedocs.io/en/latest/how_to_guide/25_choosing_vector_field_options.html): Practical guide for choosing between vector field methods and configuring them
+
+## Diagnostics
+
+- [Choosing a Diagnostic](https://sbi.readthedocs.io/en/latest/how_to_guide/14_choose_diagnostic_tool.html): Which validation tool to use
+- [Expected Coverage](https://sbi.readthedocs.io/en/latest/how_to_guide/15_expected_coverage.html): Joint posterior calibration check
+- [Simulation-Based Calibration](https://sbi.readthedocs.io/en/latest/how_to_guide/16_sbc.html): Per-parameter marginal calibration
+- [TARP](https://sbi.readthedocs.io/en/latest/how_to_guide/17_tarp.html): Calibration without density evaluation
+- [L-C2ST](https://sbi.readthedocs.io/en/latest/how_to_guide/13_diagnostics_lc2st.html): Per-observation local coverage test
+- [Model Misspecification](https://sbi.readthedocs.io/en/latest/how_to_guide/18_model_misspecification.html): Detecting if x_o is outside simulator range
+
+## Advanced Topics
+
+- [Time Series Embeddings](https://sbi.readthedocs.io/en/latest/how_to_guide/20_time_series_embedding.html): CausalCNN, Transformer for temporal data
+- [Restriction Estimator](https://sbi.readthedocs.io/en/latest/advanced_tutorials/06_restriction_estimator.html): Handling invalid simulations (NaN/Inf)
+- [Sensitivity Analysis](https://sbi.readthedocs.io/en/latest/advanced_tutorials/07_sensitivity_analysis.html): ActiveSubspace for parameter importance
+- [Posterior Parameters](https://sbi.readthedocs.io/en/latest/how_to_guide/19_posterior_parameters.html): Dataclass-based sampler configuration
+- [Experiment Tracking](https://sbi.readthedocs.io/en/latest/how_to_guide/22_experiment_tracking.html): TensorBoard, WandB, MLflow adapters
+- [Pyro Integration](https://sbi.readthedocs.io/en/latest/how_to_guide/23_using_pyro_with_sbi.html): Neural likelihoods in Pyro hierarchical models
+
+## API Reference
+
+- [Inference API](https://sbi.readthedocs.io/en/latest/api_reference.html): NPE, NLE, NRE, FMPE trainers and posteriors
+- [Installation](https://sbi.readthedocs.io/en/latest/installation.html): pip install sbi, optional dependencies
+- [Changelog](https://sbi.readthedocs.io/en/latest/changelog.html): Version history and migration notes
+- [FAQ](https://sbi.readthedocs.io/en/latest/faq.html): Common issues (leakage, NaNs, pickling, unconstrained space)
+
+## Optional
+
+- [Hodgkin-Huxley Example](https://sbi.readthedocs.io/en/latest/tutorials/Example_00_HodgkinHuxleyModel.html): Neuroscience application
+- [Decision-Making Model](https://sbi.readthedocs.io/en/latest/tutorials/Example_01_DecisionMakingModel.html): Cognitive science application
+- [GPU Training](https://sbi.readthedocs.io/en/latest/how_to_guide/07_gpu_training.html): CUDA and MPS device configuration
+- [Save and Load](https://sbi.readthedocs.io/en/latest/how_to_guide/07_save_and_load.html): Pickling posteriors, CPU_Unpickler
+- [Resume Training](https://sbi.readthedocs.io/en/latest/how_to_guide/07_resume_training.html): Checkpoint and resume
+- [MCMC Diagnostics](https://sbi.readthedocs.io/en/latest/how_to_guide/12_mcmc_diagnostics_with_arviz.html): ArviZ trace plots and R-hat
+- [Conditional Distributions](https://sbi.readthedocs.io/en/latest/how_to_guide/05_conditional_distributions.html): Conditional pairplots
+- [Importance Sampling](https://sbi.readthedocs.io/en/latest/how_to_guide/10_refine_posterior_with_importance_sampling.html): Refining posteriors
+- [Permutation-Invariant Embeddings](https://sbi.readthedocs.io/en/latest/how_to_guide/08_permutation_invariant_embeddings.html): i.i.d. data with NPE
+- [Contributing Guide](https://sbi.readthedocs.io/en/latest/contributing.html): How to contribute to sbi
diff --git a/sbi/inference/posteriors/base_posterior.py b/sbi/inference/posteriors/base_posterior.py
index 599622904..f5111cecb 100644
--- a/sbi/inference/posteriors/base_posterior.py
+++ b/sbi/inference/posteriors/base_posterior.py
@@ -93,7 +93,7 @@ def potential(
                 This can be helpful for e.g. sensitivity analysis, but increases memory
                 consumption.
         """
-        self.potential_fn.set_x(self._x_else_default_x(x))
+        self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
         theta = ensure_theta_batched(torch.as_tensor(theta))
         return self.potential_fn(
@@ -294,7 +294,7 @@ def map(
             )
 
         if self._map is None or force_update:
-            self.potential_fn.set_x(self.default_x)
+            self.potential_fn = self.potential_fn.bind(self.default_x)
             self._map = self._calculate_map(
                 num_iter=num_iter,
                 num_to_optimize=num_to_optimize,
diff --git a/sbi/inference/posteriors/ensemble_posterior.py b/sbi/inference/posteriors/ensemble_posterior.py
index 755f1cebe..fa4015f92 100644
--- a/sbi/inference/posteriors/ensemble_posterior.py
+++ b/sbi/inference/posteriors/ensemble_posterior.py
@@ -317,7 +317,7 @@ def potential(
                 This can be helpful for e.g. sensitivity analysis, but increases memory
                 consumption.
         """
-        self.potential_fn.set_x(self._x_else_default_x(x))
+        self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
         theta = ensure_theta_batched(torch.as_tensor(theta))
 
@@ -398,7 +398,7 @@ def map(
             return log_weights, maps
 
         else:
-            self.potential_fn.set_x(self._x_else_default_x(x))
+            self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
             if init_method == "posterior":
                 inits = self.sample((num_init_samples,), self._x_else_default_x(x))
@@ -488,6 +488,28 @@ def set_x(self, x_o: Optional[Tensor]):
         for comp_potential in self.potential_fns:
             comp_potential.set_x(x_o)
 
+    def bind(
+        self,
+        x_o: Tensor,
+        x_is_iid: bool = True,
+        **kwargs,
+    ) -> "EnsemblePotential":
+        """Return a new EnsemblePotential with x_o bound to all component potentials."""
+        if x_o is not None:
+            x_o = process_x(x_o).to(self.device)
+
+        bound_potentials = [
+            p.bind(x_o, x_is_iid=x_is_iid, **kwargs) for p in self.potential_fns
+        ]
+
+        return EnsemblePotential(
+            potential_fns=bound_potentials,
+            weights=self._weights,
+            prior=self.prior,
+            x_o=x_o,
+            device=self.device,
+        )
+
     def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         r"""Returns the potential for posterior-based methods.
 
diff --git a/sbi/inference/posteriors/importance_posterior.py b/sbi/inference/posteriors/importance_posterior.py
index cfbc3d2f8..fdc98a9a1 100644
--- a/sbi/inference/posteriors/importance_posterior.py
+++ b/sbi/inference/posteriors/importance_posterior.py
@@ -128,7 +128,7 @@ def log_prob(
             `len($\theta$)`-shaped log-probability.
         """
         x = self._x_else_default_x(x)
-        self.potential_fn.set_x(x)
+        self.potential_fn = self.potential_fn.bind(x)
 
         theta = ensure_theta_batched(torch.as_tensor(theta))
 
@@ -212,7 +212,7 @@ def sample(
 
         method = self.method if method is None else method
 
-        self.potential_fn.set_x(self._x_else_default_x(x))
+        self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
         if method == "sir":
             return self._sir_sample(
diff --git a/sbi/inference/posteriors/mcmc_posterior.py b/sbi/inference/posteriors/mcmc_posterior.py
index f90db67d6..fc1d254cf 100644
--- a/sbi/inference/posteriors/mcmc_posterior.py
+++ b/sbi/inference/posteriors/mcmc_posterior.py
@@ -2,7 +2,6 @@
 # under the Apache License Version 2.0, see <https://www.apache.org/licenses/>
 import inspect
 import warnings
-from copy import deepcopy
 from functools import partial
 from math import ceil
 from typing import Any, Callable, Dict, Literal, Optional, Union
@@ -237,7 +236,7 @@ def log_prob(
         warn("The log-probability is unnormalized!", stacklevel=2)
 
         x = self._x_else_default_x(x)
-        self.potential_fn.set_x(x, x_is_iid=True)
+        self.potential_fn = self.potential_fn.bind(x, x_is_iid=True)
 
         theta = ensure_theta_batched(torch.as_tensor(theta))
         return self.potential_fn(
@@ -291,7 +290,7 @@ def sample(
         """
 
         x = self._x_else_default_x(x)
-        self.potential_fn.set_x(x, x_is_iid=True)
+        self.potential_fn = self.potential_fn.bind(x, x_is_iid=True)
 
         # Replace arguments that were not passed with their default.
         method = self.method if method is None else method
@@ -451,7 +450,7 @@ def sample_batched(
         # in the order of the observations.
         x_ = x.repeat_interleave(num_chains, dim=0)
 
-        self.potential_fn.set_x(x_, x_is_iid=False)
+        self.potential_fn = self.potential_fn.bind(x_, x_is_iid=False)
         self.potential_ = self._prepare_potential(method)  # type: ignore
 
         # For each observation in the batch, we have num_chains independent chains.
@@ -662,25 +661,25 @@ def _get_initial_params_batched(
             Tensor: initial parameters, one for each chain
         """
 
-        potential_ = deepcopy(self.potential_fn)
+        potential_ = self.potential_fn
         initial_params = []
-        init_fn = self._build_mcmc_init_fn(
-            self.proposal,
-            potential_fn=potential_,
-            transform=self.theta_transform,
-            init_strategy=init_strategy,  # type: ignore
-            **kwargs,
-        )
         for xi in x:
-            # Build init function
-            potential_.set_x(xi)
+            # Build init function with bound potential for this specific xi
+            potential_bound = potential_.bind(xi)
+            init_fn = self._build_mcmc_init_fn(
+                self.proposal,
+                potential_fn=potential_bound,
+                transform=self.theta_transform,
+                init_strategy=init_strategy,  # type: ignore
+                **kwargs,
+            )
 
             # Parallelize inits for resampling or sir.
             if num_workers > 1 and (
                 init_strategy == "resample" or init_strategy == "sir"
             ):
 
-                def seeded_init_fn(seed):
+                def seeded_init_fn(seed, init_fn=init_fn):
                     torch.manual_seed(seed)
                     return init_fn()
 
diff --git a/sbi/inference/posteriors/rejection_posterior.py b/sbi/inference/posteriors/rejection_posterior.py
index 7b05160a2..92e173129 100644
--- a/sbi/inference/posteriors/rejection_posterior.py
+++ b/sbi/inference/posteriors/rejection_posterior.py
@@ -120,7 +120,7 @@ def log_prob(
         )
         warn("The log-probability is unnormalized!", stacklevel=2)
 
-        self.potential_fn.set_x(self._x_else_default_x(x))
+        self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
         theta = ensure_theta_batched(torch.as_tensor(theta))
         return self.potential_fn(
@@ -174,7 +174,7 @@ def sample(
             Samples from posterior.
         """
         num_samples = torch.Size(sample_shape).numel()
-        self.potential_fn.set_x(self._x_else_default_x(x))
+        self.potential_fn = self.potential_fn.bind(self._x_else_default_x(x))
 
         potential = partial(self.potential_fn, track_gradients=True)
 
diff --git a/sbi/inference/posteriors/vector_field_posterior.py b/sbi/inference/posteriors/vector_field_posterior.py
index 20c1990f0..3832afd75 100644
--- a/sbi/inference/posteriors/vector_field_posterior.py
+++ b/sbi/inference/posteriors/vector_field_posterior.py
@@ -521,7 +521,7 @@ def sample_batched(
         condition_dim = len(self.vector_field_estimator.condition_shape)
         batch_shape = x.shape[:-condition_dim]
         batch_size = batch_shape.numel()
-        self.potential_fn.set_x(x)
+        self.potential_fn.set_x(x, x_is_iid=batch_size > 1)
 
         max_sampling_batch_size = (
             self.max_sampling_batch_size
@@ -661,7 +661,9 @@ def map(
 
         if self._map is None or force_update:
             # rebuild coarse flow fast for MAP optimization.
-            self.potential_fn.set_x(self.default_x, atol=1e-2, rtol=1e-3, exact=True)
+            self.potential_fn.set_x(
+                self.default_x, x_is_iid=False, atol=1e-2, rtol=1e-3, exact=True
+            )
             callable_potential_fn = CallableDifferentiablePotentialFunction(
                 self.potential_fn
             )
diff --git a/sbi/inference/posteriors/vi_posterior.py b/sbi/inference/posteriors/vi_posterior.py
index e070d904f..d10162722 100644
--- a/sbi/inference/posteriors/vi_posterior.py
+++ b/sbi/inference/posteriors/vi_posterior.py
@@ -1229,7 +1229,7 @@ def _compute_amortized_elbo_loss(self, x_batch: Tensor, n_particles: int) -> Ten
         x_expanded = x_batch.repeat(n_particles, 1)
 
         # Set x_o for batched evaluation (x_is_iid=False: each θ paired with its x)
-        self.potential_fn.set_x(x_expanded, x_is_iid=False)
+        self.potential_fn = self.potential_fn.bind(x_expanded, x_is_iid=False)
         log_potential_flat = self.potential_fn(theta_flat)
 
         # Reshape: (n_particles * batch_size,) -> (n_particles, batch_size)
diff --git a/sbi/inference/potentials/base_potential.py b/sbi/inference/potentials/base_potential.py
index d24b05b94..935d0ba56 100644
--- a/sbi/inference/potentials/base_potential.py
+++ b/sbi/inference/potentials/base_potential.py
@@ -49,7 +49,7 @@ def x_is_iid(self) -> bool:
             return self._x_is_iid
         else:
             raise ValueError(
-                "No observed data is available. Use `potential_fn.set_x(x_o)`."
+                "No observed data is available. Use `potential_fn.bind(x_o)`."
             )
 
     def set_x(self, x_o: Optional[Tensor], x_is_iid: Optional[bool] = True):
@@ -66,7 +66,7 @@ def x_o(self) -> Tensor:
             return self._x_o
         else:
             raise ValueError(
-                "No observed data is available. Use `potential_fn.set_x(x_o)`."
+                "No observed data is available. Use `potential_fn.bind(x_o)`."
             )
 
     @x_o.setter
@@ -82,6 +82,20 @@ def return_x_o(self) -> Optional[Tensor]:
         """
         return self._x_o
 
+    def bind(self, x_o: Tensor, x_is_iid: bool = True) -> "BasePotential":
+        """Create new potential with x bound, without mutable state.
+
+        Args:
+            x_o: Observed data to bind.
+            x_is_iid: Whether x represents iid observations.
+
+        Returns:
+            New potential instance with x bound.
+
+        Subclasses must implement this method.
+        """
+        raise NotImplementedError(f"{self.__class__.__name__} must implement bind()")
+
     def to(self, device: Union[str, torch.device]) -> "BasePotential":
         """Move prior and x_o to the given device.
 
@@ -154,3 +168,12 @@ def __call__(self, theta, track_gradients: bool = True):
         """
         with torch.set_grad_enabled(track_gradients):
             return self.potential_fn(theta, self.x_o)
+
+    def bind(self, x_o: Tensor, x_is_iid: bool = True) -> "CustomPotentialWrapper":
+        """Create new potential with x bound, without mutable state."""
+        return CustomPotentialWrapper(
+            potential_fn=self.potential_fn,
+            prior=self.prior,
+            x_o=x_o,
+            device=self.device,
+        )
diff --git a/sbi/inference/potentials/likelihood_based_potential.py b/sbi/inference/potentials/likelihood_based_potential.py
index d2907430c..991254489 100644
--- a/sbi/inference/potentials/likelihood_based_potential.py
+++ b/sbi/inference/potentials/likelihood_based_potential.py
@@ -94,6 +94,17 @@ def to(self, device: Union[str, torch.device]) -> "LikelihoodBasedPotential":
         self.likelihood_estimator.to(device)
         return self
 
+    def bind(self, x_o: Tensor, x_is_iid: bool = True) -> "LikelihoodBasedPotential":
+        """Create new potential with x bound, without mutable state."""
+        bound = LikelihoodBasedPotential(
+            likelihood_estimator=self.likelihood_estimator,
+            prior=self.prior,
+            x_o=None,
+            device=self.device,
+        )
+        bound.set_x(x_o, x_is_iid=x_is_iid)
+        return bound
+
     def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         r"""Returns the potential $\log(p(x_o|\theta)p(\theta))$.
 
diff --git a/sbi/inference/potentials/posterior_based_potential.py b/sbi/inference/potentials/posterior_based_potential.py
index eda384626..bdaae1d9f 100644
--- a/sbi/inference/potentials/posterior_based_potential.py
+++ b/sbi/inference/potentials/posterior_based_potential.py
@@ -106,6 +106,17 @@ def set_x(self, x_o: Optional[Tensor], x_is_iid: Optional[bool] = False):
         """
         super().set_x(x_o, x_is_iid=x_is_iid)
 
+    def bind(self, x_o: Tensor, x_is_iid: bool = False) -> "PosteriorBasedPotential":
+        """Create new potential with x bound, without mutable state."""
+        bound = PosteriorBasedPotential(
+            posterior_estimator=self.posterior_estimator,
+            prior=self.prior,
+            x_o=None,
+            device=self.device,
+        )
+        bound.set_x(x_o, x_is_iid=x_is_iid)
+        return bound
+
     def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         r"""Returns the potential for posterior-based methods.
 
diff --git a/sbi/inference/potentials/ratio_based_potential.py b/sbi/inference/potentials/ratio_based_potential.py
index 844405e75..917fede47 100644
--- a/sbi/inference/potentials/ratio_based_potential.py
+++ b/sbi/inference/potentials/ratio_based_potential.py
@@ -82,6 +82,17 @@ def to(self, device: Union[str, torch.device]) -> "RatioBasedPotential":
         self.ratio_estimator.to(device)
         return self
 
+    def bind(self, x_o: Tensor, x_is_iid: bool = True) -> "RatioBasedPotential":
+        """Create new potential with x bound, without mutable state."""
+        bound = RatioBasedPotential(
+            ratio_estimator=self.ratio_estimator,
+            prior=self.prior,
+            x_o=None,
+            device=self.device,
+        )
+        bound.set_x(x_o, x_is_iid=x_is_iid)
+        return bound
+
     def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         r"""Returns the potential for likelihood-ratio-based methods.
 
diff --git a/sbi/inference/potentials/vector_field_potential.py b/sbi/inference/potentials/vector_field_potential.py
index b7ac4ba45..fbac610fd 100644
--- a/sbi/inference/potentials/vector_field_potential.py
+++ b/sbi/inference/potentials/vector_field_potential.py
@@ -61,6 +61,7 @@ def __init__(
         self.vector_field_estimator.eval()
         self.iid_method = iid_method
         self.iid_params = iid_params
+        self.neural_ode_backend = neural_ode_backend
 
         neural_ode_kwargs = neural_ode_kwargs or {}
         self.neural_ode = build_neural_ode(
@@ -128,6 +129,37 @@ def set_x(
         elif self._x_o is not None:
             self.flows = self.rebuild_flows_for_batch(**ode_kwargs)
 
+    def bind(
+        self,
+        x_o: Tensor,
+        x_is_iid: bool = False,
+        iid_method: Optional[str] = None,
+        iid_params: Optional[Dict[str, Any]] = None,
+        guidance_method: Optional[str] = None,
+        guidance_params: Optional[Dict[str, Any]] = None,
+        **ode_kwargs,
+    ) -> "VectorFieldBasedPotential":
+        """Create new potential with x bound, without mutable state."""
+        bound = VectorFieldBasedPotential(
+            vector_field_estimator=self.vector_field_estimator,
+            prior=self.prior,
+            x_o=None,
+            device=self.device,
+            iid_method=self.iid_method,
+            iid_params=self.iid_params,
+            neural_ode_backend=self.neural_ode_backend,
+        )
+        bound.set_x(
+            x_o,
+            x_is_iid=x_is_iid,
+            iid_method=iid_method,
+            iid_params=iid_params,
+            guidance_method=guidance_method,
+            guidance_params=guidance_params,
+            **ode_kwargs,
+        )
+        return bound
+
     def __call__(
         self,
         theta: Tensor,
diff --git a/sbi/utils/conditional_density_utils.py b/sbi/utils/conditional_density_utils.py
index 0d48efedb..a42e6b4ed 100644
--- a/sbi/utils/conditional_density_utils.py
+++ b/sbi/utils/conditional_density_utils.py
@@ -412,7 +412,7 @@ def x_is_iid(self) -> bool:
             return self._x_is_iid
         else:
             raise ValueError(
-                "No observed data is available. Use `potential_fn.set_x(x_o)`."
+                "No observed data is available. Use `potential_fn.bind(x_o)`."
             )
 
     def set_x(self, x_o: Optional[Tensor], x_is_iid: Optional[bool] = True):
@@ -420,7 +420,15 @@ def set_x(self, x_o: Optional[Tensor], x_is_iid: Optional[bool] = True):
         if x_o is not None:
             x_o = process_x(x_o).to(self.device)
         self._x_is_iid = x_is_iid
-        self.potential_fn.set_x(x_o, x_is_iid=x_is_iid)
+        self.potential_fn = self.potential_fn.bind(x_o, x_is_iid=x_is_iid)
+
+    def bind(self, x_o: Tensor, x_is_iid: bool = True) -> "ConditionedPotential":
+        """Create new potential with x bound, without mutable state."""
+        return ConditionedPotential(
+            potential_fn=self.potential_fn.bind(x_o, x_is_iid),
+            condition=self.condition,
+            dims_to_sample=self.dims_to_sample,
+        )
 
     @property
     def x_o(self) -> Tensor:
diff --git a/sbi/utils/torchutils.py b/sbi/utils/torchutils.py
index f8ed0f7cd..f0e97d534 100644
--- a/sbi/utils/torchutils.py
+++ b/sbi/utils/torchutils.py
@@ -659,6 +659,7 @@ def _base_recursor(
     key: Optional[str] = None,
     check: Callable[..., bool] = lambda obj: False,
     action: Callable[..., object] = lambda obj: obj,
+    _active: Optional[set[int]] = None,
 ):
     """Recursive function that traverses objects (e.g. Distributions) and applies
     an action to any encountered object that passes the check.
@@ -673,7 +674,17 @@ def _base_recursor(
             If the check evaluates to True, then ``action`` is applied.
         action: A function that specifies an operation on an object and returns
             a modified version.
+        _active: Object identities on the active recursion path. Used internally
+            to avoid infinite recursion in cyclic object graphs.
     """
+    _active_holder: Optional[set[int]] = _active
+    if _active_holder is None:
+        _active_holder = set()
+    obj_id = id(obj)
+    if obj_id in _active_holder:
+        return
+    _active_holder.add(obj_id)
+
     if isinstance(obj, Module) and check(obj):
         action(obj)
     elif isinstance(obj, (Dict, OrderedDict)):
@@ -681,29 +692,43 @@ def _base_recursor(
             if check(o):
                 obj[k] = action(o)
             else:
-                _base_recursor(o, parent=obj, key=k, check=check, action=action)
+                _base_recursor(
+                    o,
+                    parent=obj,
+                    key=k,
+                    check=check,
+                    action=action,
+                    _active=_active_holder,
+                )
     elif isinstance(obj, type):
         # Skip class/type objects to avoid modifying immutable C extension types
         # (e.g. torch.LongTensor) which fail on Python 3.13+.
-        return
+        pass
     elif hasattr(obj, "__dict__"):
         for k, o in obj.__dict__.items():
             if check(o):
                 setattr(obj, k, action(o))
             else:
-                _base_recursor(o, parent=obj, key=k, check=check, action=action)
+                _base_recursor(
+                    o,
+                    parent=obj,
+                    key=k,
+                    check=check,
+                    action=action,
+                    _active=_active_holder,
+                )
     elif isinstance(obj, (List, Tuple, Generator)):
         new_obj = []
         for o in obj:
             if check(o):
                 new_obj.append(action(o))
             else:
-                _base_recursor(o, check=check, action=action)
+                _base_recursor(o, check=check, action=action, _active=_active_holder)
                 new_obj.append(o)
         if parent is not None and key is not None:
             setattr(parent, key, type(obj)(new_obj))  # type: ignore
-    else:
-        return
+
+    _active_holder.remove(obj_id)
 
 
 def move_all_tensor_to_device(obj: object, device: Union[str, torch.device]) -> None:
diff --git a/sbi/utils/user_input_checks_utils.py b/sbi/utils/user_input_checks_utils.py
index dbd8a1d5e..9a1f96124 100644
--- a/sbi/utils/user_input_checks_utils.py
+++ b/sbi/utils/user_input_checks_utils.py
@@ -2,6 +2,7 @@
 # under the Apache License Version 2.0, see <https://www.apache.org/licenses/>
 
 import warnings
+from copy import deepcopy
 from typing import Dict, Optional, Sequence, Union
 
 import torch
@@ -181,18 +182,15 @@ def __init__(
         event_shape=torch.Size(),
         validate_args=None,
     ):
+        self.prior = prior
+        self.device = None
+        self.return_type = return_type
         super().__init__(
             batch_shape=batch_shape,
             event_shape=event_shape,
-            validate_args=(
-                prior._validate_args if validate_args is None else validate_args
-            ),
+            validate_args=False,
         )
 
-        self.prior = prior
-        self.device = None
-        self.return_type = return_type
-
     def log_prob(self, value) -> Tensor:
         return torch.as_tensor(
             self.prior.log_prob(value),
@@ -236,6 +234,15 @@ def to(self, device: Union[str, torch.device]) -> None:
         self.prior = move_distribution_to_device(self.prior, device)
         self.device = device
 
+    def __deepcopy__(self, memo):
+        """Ensure prior attribute is preserved during deepcopy."""
+        cls = self.__class__
+        result = cls.__new__(cls)
+        memo[id(self)] = result
+        for k, v in self.__dict__.items():
+            setattr(result, k, deepcopy(v, memo))
+        return result
+
 
 class MultipleIndependent(Distribution):
     """Wrap a sequence of PyTorch distributions into a joint PyTorch distribution."""
@@ -434,6 +441,15 @@ def to(self, device: Union[str, torch.device]) -> None:
             self.dists[i] = move_distribution_to_device(self.dists[i], device)
         self.device = device
 
+    def __deepcopy__(self, memo):
+        """Ensure dists attribute is preserved during deepcopy."""
+        cls = self.__class__
+        result = cls.__new__(cls)
+        memo[id(self)] = result
+        for k, v in self.__dict__.items():
+            setattr(result, k, deepcopy(v, memo))
+        return result
+
 
 def build_support(
     lower_bound: Optional[Tensor] = None, upper_bound: Optional[Tensor] = None
@@ -523,15 +539,13 @@ class OneDimPriorWrapper(Distribution):
     """
 
     def __init__(self, prior: Distribution, validate_args=None) -> None:
+        self.prior = prior
+        self.device = None
         super().__init__(
             batch_shape=prior.batch_shape,
             event_shape=prior.event_shape,
-            validate_args=(
-                prior._validate_args if validate_args is None else validate_args
-            ),
+            validate_args=False,
         )
-        self.prior = prior
-        self.device = None
 
     def to(self, device: Union[str, torch.device]) -> None:
         """
@@ -568,3 +582,12 @@ def mean(self) -> Tensor:
     @property
     def variance(self) -> Tensor:
         return self.prior.variance
+
+    def __deepcopy__(self, memo):
+        """Ensure prior attribute is preserved during deepcopy."""
+        cls = self.__class__
+        result = cls.__new__(cls)
+        memo[id(self)] = result
+        for k, v in self.__dict__.items():
+            setattr(result, k, deepcopy(v, memo))
+        return result
diff --git a/tests/inference_on_device_test.py b/tests/inference_on_device_test.py
index 395f09a71..a56f323fa 100644
--- a/tests/inference_on_device_test.py
+++ b/tests/inference_on_device_test.py
@@ -396,6 +396,12 @@ def __call__(self, theta, **kwargs):
         def allow_iid_x(self) -> bool:
             return True
 
+        def bind(self, x_o: torch.Tensor, x_is_iid: bool = True) -> "FakePotential":
+            """Create new potential with x bound, without mutable state."""
+            bound = FakePotential(prior=self.prior, device=self.device)
+            bound.set_x(x_o, x_is_iid=x_is_iid)
+            return bound
+
     potential_fn = FakePotential(
         prior=MultivariateNormal(
             zeros(num_dim, device=device), eye(num_dim, device=device)
@@ -450,6 +456,12 @@ def __call__(self, theta, **kwargs):
         def allow_iid_x(self) -> bool:
             return True
 
+        def bind(self, x_o: torch.Tensor, x_is_iid: bool = True) -> "FakePotential":
+            """Create new potential with x bound, without mutable state."""
+            bound = FakePotential(prior=self.prior, device=self.device)
+            bound.set_x(x_o, x_is_iid=x_is_iid)
+            return bound
+
     potential_fn = FakePotential(prior=prior, device=device)
 
     # Generate mock simulation data on device
diff --git a/tests/torchutils_test.py b/tests/torchutils_test.py
index b60c36237..5be20b51f 100644
--- a/tests/torchutils_test.py
+++ b/tests/torchutils_test.py
@@ -5,6 +5,8 @@
 
 from __future__ import annotations
 
+from copy import deepcopy
+
 import numpy as np
 import pytest
 import torch
@@ -16,6 +18,49 @@
 from tests.test_utils import kl_d_via_monte_carlo
 
 
+def test_base_recursor_handles_cyclic_object_graph():
+    class CyclicObject:
+        pass
+
+    root = CyclicObject()
+    tensor = torch.tensor(1.0)
+    root.tensor = tensor
+    root.self = root
+    root.mapping = {"root": root, "tensor": tensor}
+
+    processed = []
+
+    def process(obj):
+        processed.append(obj)
+        return obj
+
+    torchutils._base_recursor(root, check=torch.is_tensor, action=process)
+
+    assert len(processed) == 2
+    assert all(obj is tensor for obj in processed)
+
+
+def test_base_recursor_processes_aliased_containers():
+    class AliasedObject:
+        pass
+
+    root = AliasedObject()
+    tensor = torch.tensor(1.0, requires_grad=True) * 2
+    shared = [tensor]
+    root.first = shared
+    root.second = shared
+
+    torchutils._base_recursor(
+        root,
+        check=lambda obj: torch.is_tensor(obj) and not obj.is_leaf,
+        action=lambda obj: obj.detach(),
+    )
+
+    assert root.first[0].is_leaf
+    assert root.second[0].is_leaf
+    deepcopy(root)
+
+
 # XXX move to pytest? - investigate how to derive from TorchTestCase
 class TorchUtilsTest(torchtestcase.TorchTestCase):
     def test_split_leading_dim(self):
diff --git a/tests/vi_test.py b/tests/vi_test.py
index e1327e56a..f3f187ce9 100644
--- a/tests/vi_test.py
+++ b/tests/vi_test.py
@@ -57,6 +57,12 @@ def __call__(self, theta, **kwargs):
     def allow_iid_x(self) -> bool:
         return True
 
+    def bind(self, x_o: torch.Tensor, x_is_iid: bool = True) -> "FakePotential":
+        """Create new potential with x bound, without mutable state."""
+        bound = FakePotential(prior=self.prior, device=self.device)
+        bound.set_x(x_o, x_is_iid=x_is_iid)
+        return bound
+
 
 def make_tractable_potential(target_distribution, prior):
     """Create a potential function from a known target distribution."""
@@ -70,6 +76,14 @@ def __call__(self, theta, **kwargs):
         def allow_iid_x(self) -> bool:
             return True
 
+        def bind(
+            self, x_o: torch.Tensor, x_is_iid: bool = True
+        ) -> "TractablePotential":
+            """Create new potential with x bound, without mutable state."""
+            bound = TractablePotential(prior=self.prior, device=self.device)
+            bound.set_x(x_o, x_is_iid=x_is_iid)
+            return bound
+
     return TractablePotential(prior=prior)
 
 
diff --git a/uv.lock b/uv.lock
index 4afc6c03a..9f0cbed83 100644
--- a/uv.lock
+++ b/uv.lock
@@ -815,45 +815,51 @@ wheels = [
 
 [[package]]
 name = "cuda-toolkit"
-version = "13.0.2"
+version = "13.0.3.0"
 source = { registry = "https://pypi.org/simple" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/57/b2/453099f5f3b698d7d0eab38916aac44c7f76229f451709e2eb9db6615dcd/cuda_toolkit-13.0.2-py2.py3-none-any.whl", hash = "sha256:b198824cf2f54003f50d64ada3a0f184b42ca0846c1c94192fa269ecd97a66eb", size = 2364, upload-time = "2025-12-19T23:24:07.328Z" },
+    { url = "https://files.pythonhosted.org/packages/d1/c7/a79086a62c98befcdb8349656c6f114e2db3b8b2422f6e25c97a7f2a9a3c/cuda_toolkit-13.0.3.0-py2.py3-none-any.whl", hash = "sha256:d693caaa261214ddd7dbb60d68e71cbed884e68c2be7509778f3051da0b91c3f", size = 2512, upload-time = "2026-04-14T00:50:08.173Z" },
 ]
 
 [package.optional-dependencies]
 cublas = [
-    { name = "nvidia-cublas", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-cublas", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
+    { name = "nvidia-cuda-nvrtc", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 cudart = [
-    { name = "nvidia-cuda-runtime", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-cuda-runtime", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 cufft = [
-    { name = "nvidia-cufft", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-cufft", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
+    { name = "nvidia-nvjitlink", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 cufile = [
-    { name = "nvidia-cufile", marker = "sys_platform == 'linux'" },
+    { name = "nvidia-cufile", marker = "(platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 cupti = [
-    { name = "nvidia-cuda-cupti", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-cuda-cupti", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 curand = [
-    { name = "nvidia-curand", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-curand", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
 ]
 cusolver = [
-    { name = "nvidia-cusolver", marker = "(python_full_version < '3.11' and sys_platform == 'win32') or sys_platform == 'linux'" },
+    { name = "nvidia-cublas", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
+    { name = "nvidia-cusolver", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
+    { name = "nvidia-cusparse", marker = "(python_full_version < '3.11' and platform_machine == 'AMD64' and sys_platform == 'win32') or (platform_machine == 'aarch64' and sys_platform == 'linux') or (platform_machine == 'x86_64' and sys_platform == 'linux')" },
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