diff --git a/tests/test_optim.py b/tests/test_optim.py
new file mode 100644
index 00000000..8c3658db
--- /dev/null
+++ b/tests/test_optim.py
@@ -0,0 +1,22 @@
+import torch
+
+import uqlib
+
+
+def test_optim():
+    optimizer_cls = torch.optim.SGD
+    lr = 0.1
+
+    def loss_fn(p, b):
+        return torch.sum(p**2), torch.tensor([])
+
+    transform = uqlib.optim.build(loss_fn, optimizer_cls, lr=lr)
+
+    params = torch.tensor([1.0], requires_grad=True)
+    state = transform.init(params)
+
+    for _ in range(100):
+        state = transform.update(state, torch.tensor([1.0]))
+
+    assert state.loss < 1e-3
+    assert state.params < 1e-3
diff --git a/tests/test_torchopt.py b/tests/test_torchopt.py
new file mode 100644
index 00000000..7a1b9956
--- /dev/null
+++ b/tests/test_torchopt.py
@@ -0,0 +1,22 @@
+import torch
+import torchopt
+
+import uqlib
+
+
+def test_torchopt():
+    optimizer = torchopt.sgd(lr=0.1)
+
+    def loss_fn(p, b):
+        return torch.sum(p**2), torch.tensor([])
+
+    transform = uqlib.torchopt.build(loss_fn, optimizer)
+
+    params = torch.tensor([1.0], requires_grad=True)
+    state = transform.init(params)
+
+    for _ in range(100):
+        state = transform.update(state, torch.tensor([1.0]))
+
+    assert state.loss < 1e-3
+    assert state.params < 1e-3
diff --git a/uqlib/__init__.py b/uqlib/__init__.py
index 0edd023d..3d7f35cd 100644
--- a/uqlib/__init__.py
+++ b/uqlib/__init__.py
@@ -3,6 +3,8 @@
 from uqlib import sgmcmc
 from uqlib import types
 from uqlib import vi
+from uqlib import optim
+from uqlib import torchopt
 
 from uqlib.utils import model_to_function
 from uqlib.utils import linearized_forward_diag
diff --git a/uqlib/optim.py b/uqlib/optim.py
new file mode 100644
index 00000000..774b2ab9
--- /dev/null
+++ b/uqlib/optim.py
@@ -0,0 +1,103 @@
+from typing import Type, NamedTuple, Any
+from functools import partial
+import torch
+
+from uqlib.types import TensorTree, Transform, LogProbFn
+
+
+class OptimState(NamedTuple):
+    """State of an optimizer.
+
+    Args:
+        params: Parameters to be optimised.
+        optimizer: torch.optim optimizer instance.
+        loss: Loss value.
+        aux: Auxiliary information from the loss function call.
+    """
+
+    params: TensorTree
+    optimizer: torch.optim.Optimizer
+    loss: torch.tensor = torch.tensor(0.0)
+    aux: Any = None
+
+
+def init(
+    params: TensorTree,
+    optimizer_cls: Type[torch.optim.Optimizer],
+    *args: Any,
+    **kwargs: Any,
+) -> OptimState:
+    """Initialise an optimizer.
+
+    Args:
+        params: Parameters to be optimised.
+        optimizer_cls: Optimizer class from torch.optim.
+        *args: Positional arguments to pass to the optimizer class.
+        **kwargs: Keyword arguments to pass to the optimizer class.
+
+    Returns:
+        Initial OptimState.
+    """
+    opt_params = [params] if isinstance(params, torch.Tensor) else params
+
+    optimizer = optimizer_cls(opt_params, *args, **kwargs)
+    return OptimState(params, optimizer)
+
+
+def update(
+    state: OptimState,
+    batch: TensorTree,
+    loss_fn: LogProbFn,
+    inplace: bool = True,
+) -> OptimState:
+    """Perform a single update step of the optimizer.
+
+    Args:
+        state: Current optimizer state.
+        batch: Input data to loss_fn.
+        loss_fn: Function that takes the parameters and returns the loss.
+            of the form `loss, aux = fn(params, batch)`.
+        inplace: Whether to update the parameters in place.
+            inplace=False not supported for uqlib.optim
+
+    Returns:
+        Updated OptimState.
+    """
+    if not inplace:
+        raise NotImplementedError("inplace=False not supported for uqlib.optim")
+    state.optimizer.zero_grad()
+    loss, aux = loss_fn(state.params, batch)
+    loss.backward()
+    state.optimizer.step()
+    return OptimState(state.params, state.optimizer, state.loss.detach(), aux)
+
+
+def build(
+    loss_fn: LogProbFn,
+    optimizer: Type[torch.optim.Optimizer],
+    **kwargs: Any,
+) -> Transform:
+    """Builds an optimizer transform from torch.optim.
+
+    Example usage:
+
+    ```
+    transform = build(loss_fn, torch.optim.Adam, lr=0.1)
+    state = transform.init(params)
+
+    for batch in dataloader:
+        state = transform.update(state, batch)
+    ```
+
+    Arg:
+        loss_fn: Function that takes the parameters and returns the loss.
+            of the form `loss, aux = fn(params, batch)`.
+        optimizer: Optimizer class from torch.optim.
+        **kwargs: Keyword arguments to pass to the optimizer class.
+
+    Returns:
+        Optimizer transform (uqlib.types.Transform instance).
+    """
+    init_fn = partial(init, optimizer_cls=optimizer, **kwargs)
+    update_fn = partial(update, loss_fn=loss_fn)
+    return Transform(init_fn, update_fn)
diff --git a/uqlib/torchopt.py b/uqlib/torchopt.py
new file mode 100644
index 00000000..57216c42
--- /dev/null
+++ b/uqlib/torchopt.py
@@ -0,0 +1,100 @@
+from typing import NamedTuple, Any
+from functools import partial
+import torch
+import torchopt
+
+from uqlib.types import TensorTree, Transform, LogProbFn
+
+
+class TorchOptState(NamedTuple):
+    """State of a TorchOpt optimizer.
+
+    Args:
+        params: Parameters to be optimised.
+        opt_state: TorchOpt optimizer state.
+        loss: Loss value.
+        aux: Auxiliary information from the loss function call.
+    """
+
+    params: TensorTree
+    opt_state: torch.optim.Optimizer
+    loss: torch.tensor = torch.tensor(0.0)
+    aux: Any = None
+
+
+def init(
+    params: TensorTree,
+    optimizer: torchopt.base.GradientTransformation,
+) -> TorchOptState:
+    """Initialise a TorchOpt optimizer.
+
+    Args:
+        params: Parameters to be optimised.
+        optimizer: TorchOpt functional optimizer.
+            Make sure to use lower case like torchopt.adam()
+
+    Returns:
+        Initial TorchOptState.
+    """
+    opt_state = optimizer.init(params)
+    return TorchOptState(params, opt_state)
+
+
+def update(
+    state: TorchOptState,
+    batch: TensorTree,
+    loss_fn: LogProbFn,
+    optimizer: torchopt.base.GradientTransformation,
+    inplace: bool = True,
+) -> TorchOptState:
+    """Update the optimizer state.
+
+    Args:
+        state: Current state.
+        batch: Batch of data.
+        loss_fn: Loss function.
+        optimizer: TorchOpt functional optimizer.
+            Make sure to use lower case like torchopt.adam()
+        inplace: Whether to update the state in place.
+
+    Returns:
+        Updated state.
+    """
+    params = state.params
+    opt_state = state.opt_state
+    with torch.no_grad():
+        grads, (loss, aux) = torch.func.grad_and_value(loss_fn, has_aux=True)(
+            params, batch
+        )
+    updates, opt_state = optimizer.update(grads, opt_state)
+    params = torchopt.apply_updates(params, updates, inplace=inplace)
+    return TorchOptState(params, opt_state, loss, aux)
+
+
+def build(
+    loss_fn: LogProbFn,
+    optimizer: torchopt.base.GradientTransformation,
+) -> Transform:
+    """Build a TorchOpt optimizer transformation.
+
+    Example usage:
+
+    ```
+    transform = build(loss_fn, torchopt.adam(lr=0.1))
+    state = transform.init(params)
+
+    for batch in dataloader:
+        state = transform.update(state, batch)
+    ```
+
+    Args:
+        loss_fn: Loss function.
+        optimizer: TorchOpt functional optimizer.
+            Make sure to use lower case like torchopt.adam()
+
+    Returns:
+        Torchopt optimizer transform (uqlib.types.Transform instance).
+    """
+    init_fn = partial(init, optimizer=optimizer)
+    update_fn = partial(update, optimizer=optimizer, loss_fn=loss_fn)
+    return Transform(init_fn, update_fn)