diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 9ac9eff143..3140b8857b 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -118,6 +118,7 @@ jobs:
             tests/logprob/test_order.py
             tests/logprob/test_rewriting.py
             tests/logprob/test_scan.py
+            tests/logprob/test_set_subtensor.py
             tests/logprob/test_tensor.py
             tests/logprob/test_transform_value.py
             tests/logprob/test_transforms.py
diff --git a/pymc/logprob/__init__.py b/pymc/logprob/__init__.py
index bed9ee3a9c..6b5a1bfc57 100644
--- a/pymc/logprob/__init__.py
+++ b/pymc/logprob/__init__.py
@@ -50,6 +50,7 @@
 import pymc.logprob.mixture
 import pymc.logprob.order
 import pymc.logprob.scan
+import pymc.logprob.set_subtensor
 import pymc.logprob.tensor
 import pymc.logprob.transforms
 
diff --git a/pymc/logprob/set_subtensor.py b/pymc/logprob/set_subtensor.py
new file mode 100644
index 0000000000..8b3ec0df1e
--- /dev/null
+++ b/pymc/logprob/set_subtensor.py
@@ -0,0 +1,215 @@
+#   Copyright 2024 The PyMC Developers
+#
+#   Licensed under the Apache License, Version 2.0 (the "License");
+#   you may not use this file except in compliance with the License.
+#   You may obtain a copy of the License at
+#
+#       http://www.apache.org/licenses/LICENSE-2.0
+#
+#   Unless required by applicable law or agreed to in writing, software
+#   distributed under the License is distributed on an "AS IS" BASIS,
+#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#   See the License for the specific language governing permissions and
+#   limitations under the License.
+from pytensor.graph.basic import Variable
+from pytensor.graph.rewriting.basic import node_rewriter
+from pytensor.tensor import eq
+from pytensor.tensor.subtensor import (
+    AdvancedIncSubtensor,
+    AdvancedIncSubtensor1,
+    IncSubtensor,
+    indices_from_subtensor,
+)
+from pytensor.tensor.type import TensorType
+from pytensor.tensor.type_other import NoneTypeT
+
+from pymc.logprob.abstract import MeasurableOp, _logprob, _logprob_helper
+from pymc.logprob.checks import MeasurableCheckAndRaise
+from pymc.logprob.rewriting import measurable_ir_rewrites_db
+from pymc.logprob.utils import (
+    check_potential_measurability,
+    dirac_delta,
+    filter_measurable_variables,
+)
+
+
+class MeasurableSetSubtensor(IncSubtensor, MeasurableOp):
+    """Measurable SetSubtensor Op."""
+
+    def __str__(self):
+        return f"Measurable{super().__str__()}"
+
+
+class MeasurableAdvancedSetSubtensor(AdvancedIncSubtensor, MeasurableOp):
+    """Measurable AdvancedSetSubtensor Op."""
+
+    def __str__(self):
+        return f"Measurable{super().__str__()}"
+
+
+set_subtensor_does_not_broadcast = MeasurableCheckAndRaise(
+    exc_type=NotImplementedError,
+    msg="Measurable SetSubtensor not supported when set value is broadcasted.",
+)
+
+
+@node_rewriter(tracks=[IncSubtensor, AdvancedIncSubtensor1, AdvancedIncSubtensor])
+def find_measurable_set_subtensor(fgraph, node) -> list | None:
+    """Find `SetSubtensor` for which a `logprob` can be computed."""
+
+    if isinstance(node.op, MeasurableOp):
+        return None
+
+    if not node.op.set_instead_of_inc:
+        return None
+
+    x, y, *idx_elements = node.inputs
+
+    measurable_inputs = filter_measurable_variables([x, y])
+
+    if y not in measurable_inputs:
+        return None
+
+    if x not in measurable_inputs:
+        # x is potentially measurable, wait for it's logprob IR to be inferred
+        if check_potential_measurability([x]):
+            return None
+        # x has no link to measurable variables, so it's value should be constant
+        else:
+            x = dirac_delta(x, rtol=0, atol=0)
+
+    if check_potential_measurability(idx_elements):
+        return None
+
+    if isinstance(node.op, IncSubtensor):
+        measurable_class = MeasurableSetSubtensor
+        idx = indices_from_subtensor(idx_elements, node.op.idx_list)
+    else:
+        measurable_class = MeasurableAdvancedSetSubtensor
+        idx = tuple(idx_elements)
+
+    # Check that y is not certainly broadcasted.
+    indexed_block = x[idx]
+    missing_y_dims = indexed_block.type.ndim - y.type.ndim
+    y_bcast = [True] * missing_y_dims + list(y.type.broadcastable)
+    if any(
+        y_dim_bcast and indexed_block_dim_len not in (None, 1)
+        for y_dim_bcast, indexed_block_dim_len in zip(
+            y_bcast, indexed_block.type.shape, strict=True
+        )
+    ):
+        return None
+
+    measurable_set_subtensor = measurable_class(**node.op._props_dict())(x, y, *idx_elements)
+
+    # Often with indexing we don't know the static shape of the indexed block.
+    # And, what's more, the indexing operations actually support runtime broadcasting.
+    # As the logp is not valid under broadcasting, we have to add a runtime check.
+    # This will hopefully be removed during shape inference when not violated.
+    potential_broadcasted_dims = [
+        i
+        for i, (y_bcast_dim, indexed_block_dim_len) in enumerate(
+            zip(y_bcast, indexed_block.type.shape)
+        )
+        if y_bcast_dim and indexed_block_dim_len is None
+    ]
+    if potential_broadcasted_dims:
+        indexed_block_shape = tuple(indexed_block.shape)
+        measurable_set_subtensor = set_subtensor_does_not_broadcast(
+            measurable_set_subtensor,
+            *(eq(indexed_block_shape[i], 1) for i in potential_broadcasted_dims),
+        )
+
+    return [measurable_set_subtensor]
+
+
+measurable_ir_rewrites_db.register(
+    find_measurable_set_subtensor.__name__,
+    find_measurable_set_subtensor,
+    "basic",
+    "set_subtensor",
+)
+
+
+def indexed_dims(idx) -> list[int | None]:
+    """Return the indices of the dimensions of the indexed tensor that are being indexed."""
+    dims = []
+    idx_counter = 0
+    for idx_elem in idx:
+        if isinstance(idx_elem, Variable) and isinstance(idx_elem.type, NoneTypeT):
+            # None in indexes correspond to newaxis, and don't map to any existing dimension
+            dims.append(None)
+
+        elif (
+            isinstance(idx_elem, Variable)
+            and isinstance(idx_elem.type, TensorType)
+            and idx_elem.type.dtype == "bool"
+        ):
+            # Boolean indexes map to as many dimensions as the mask has
+            for i in range(idx_elem.type.ndim):
+                dims.append(idx_counter)
+                idx_counter += 1
+        else:
+            dims.append(idx_counter)
+            idx_counter += 1
+
+    return dims
+
+
+@_logprob.register(MeasurableSetSubtensor)
+@_logprob.register(MeasurableAdvancedSetSubtensor)
+def logprob_setsubtensor(op, values, x, y, *idx_elements, **kwargs):
+    """Compute the log-likelihood graph for a `SetSubtensor`.
+
+    For a generative graph like:
+        o = zeros(2)
+        x = o[0].set(X)
+        y = x[1].set(Y)
+
+    The log-likelihood graph is:
+        logp(y, value) = (
+            logp(x, value)
+            [1].set(logp(y, value[1]))
+        )
+
+    Unrolling the logp(x, value) gives:
+        logp(y, value) = (
+            DiracDelta(zeros(2), value)  # Irrelevant if all entries are set
+            [0].set(logp(x, value[0]))
+            [1].set(logp(y, value[1]))
+        )
+    """
+    [value] = values
+    if isinstance(op, MeasurableSetSubtensor):
+        # For basic indexing we have to recreate the index from the input list
+        idx = indices_from_subtensor(idx_elements, op.idx_list)
+    else:
+        # For advanced indexing we can use the idx_elements directly
+        idx = tuple(idx_elements)
+
+    x_logp = _logprob_helper(x, value)
+    y_logp = _logprob_helper(y, value[idx])
+
+    y_ndim_supp = x[idx].type.ndim - y_logp.type.ndim
+    x_ndim_supp = x.type.ndim - x_logp.type.ndim
+    ndim_supp = max(y_ndim_supp, x_ndim_supp)
+    if ndim_supp > 0:
+        # Multivariate logp only valid if we are not doing indexing along the reduced dimensions
+        # Otherwise we don't know if successive writings are overlapping or not
+        core_dims = set(range(x.type.ndim)[-ndim_supp:])
+        if set(indexed_dims(idx)) & core_dims:
+            # When we have IR meta-info about support_ndim, we can fail at the rewriting stage
+            raise NotImplementedError(
+                "Indexing along core dimensions of multivariate SetSubtensor not supported"
+            )
+
+        ndim_supp_diff = y_ndim_supp - x_ndim_supp
+        if ndim_supp_diff > 0:
+            # In this case y_logp will have fewer dimensions than x_logp after indexing, so we need to reduce x before indexing.
+            x_logp = x_logp.sum(axis=tuple(range(-ndim_supp_diff, 0)))
+        elif ndim_supp_diff < 0:
+            # In this case x_logp will have fewer dimensions than y_logp after indexing, so we need to reduce y before indexing.
+            y_logp = y_logp.sum(axis=tuple(range(ndim_supp_diff, 0)))
+
+    out_logp = x_logp[idx].set(y_logp)
+    return out_logp
diff --git a/pymc/logprob/utils.py b/pymc/logprob/utils.py
index 3b3fc4737c..14030155ca 100644
--- a/pymc/logprob/utils.py
+++ b/pymc/logprob/utils.py
@@ -285,7 +285,7 @@ def diracdelta_logprob(op, values, const_value, **kwargs):
     else:
         # Loose equality, more expensive logp
         match = pt.isclose(values, const_value, rtol=op.rtol, atol=op.atol)
-    return pt.switch(match, 0.0, -np.inf)
+    return pt.switch(match, 0.0, -np.inf).astype(value.type.dtype)
 
 
 def find_negated_var(var):
diff --git a/tests/logprob/test_set_subtensor.py b/tests/logprob/test_set_subtensor.py
new file mode 100644
index 0000000000..d3eedea3aa
--- /dev/null
+++ b/tests/logprob/test_set_subtensor.py
@@ -0,0 +1,158 @@
+#   Copyright 2024 The PyMC Developers
+#
+#   Licensed under the Apache License, Version 2.0 (the "License");
+#   you may not use this file except in compliance with the License.
+#   You may obtain a copy of the License at
+#
+#       http://www.apache.org/licenses/LICENSE-2.0
+#
+#   Unless required by applicable law or agreed to in writing, software
+#   distributed under the License is distributed on an "AS IS" BASIS,
+#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#   See the License for the specific language governing permissions and
+#   limitations under the License.
+import numpy as np
+import pytensor
+import pytensor.tensor as pt
+import pytest
+
+from pymc.distributions import Beta, Dirichlet, MvNormal, MvStudentT, Normal, StudentT
+from pymc.logprob.basic import logp
+
+
+@pytest.mark.parametrize("univariate", [True, False])
+def test_complete_set_subtensor(univariate):
+    if univariate:
+        rv0 = Normal.dist(mu=-10)
+        rv1 = StudentT.dist(nu=3, mu=0)
+        rv2 = Normal.dist(mu=10, sigma=3)
+        rv34 = Beta.dist(alpha=[np.pi, np.e], beta=[1, 1])
+        base = pt.empty((5,))
+        test_val = [2, 0, -2, 0.25, 0.5]
+    else:
+        rv0 = MvNormal.dist(mu=[-11, -9], cov=pt.eye(2))
+        rv1 = MvStudentT.dist(nu=3, mu=[-1, 1], cov=pt.eye(2))
+        rv2 = MvNormal.dist(mu=[9, 11], cov=pt.eye(2) * 3)
+        rv34 = Dirichlet.dist(a=[[np.pi, 1], [np.e, 1]])
+        base = pt.empty((3, 2))
+        test_val = [[2, 0], [0, -2], [-2, 2], [0.25, 0.75], [0.5, 0.5]]
+
+    # fmt: off
+    rv = (
+        # Boolean indexing
+        base[np.array([True, False, False, False, False])].set(rv0)
+        # Slice indexing
+        [1:2].set(rv1)
+        # Integer indexing
+        [2].set(rv2)
+        # Vector indexing
+        [[3, 4]].set(rv34)
+    )
+    # fmt: on
+    ref_rv = pt.join(0, [rv0], [rv1], [rv2], rv34)
+
+    np.testing.assert_allclose(
+        logp(rv, test_val).eval(),
+        logp(ref_rv, test_val).eval(),
+    )
+
+
+def test_partial_set_subtensor():
+    rv123 = Normal.dist(mu=[-10, 0, 10])
+
+    # When base is empty, it doesn't matter what the missing values are
+    base = pt.empty((5,))
+    rv = base[:3].set(rv123)
+
+    np.testing.assert_allclose(
+        logp(rv, [0, 0, 0, 1, np.pi]).eval(),
+        [*logp(rv123, [0, 0, 0]).eval(), 0, 0],
+    )
+
+    # Otherwise they should match
+    base = pt.ones((5,))
+    rv = base[:3].set(rv123)
+
+    np.testing.assert_allclose(
+        logp(rv, [0, 0, 0, 1, np.pi]).eval(),
+        [*logp(rv123, [0, 0, 0]).eval(), 0, -np.inf],
+    )
+
+
+def test_overwrite_set_subtensor():
+    """Test that order of overwriting in the generative graph is respected."""
+    x = Normal.dist(mu=[0, 1, 2])
+    y = x[1:].set(Normal.dist([10, 20]))
+    z = y[2:].set(Normal.dist([300]))
+
+    np.testing.assert_allclose(
+        logp(z, [0, 0, 0]).eval(),
+        logp(Normal.dist([0, 10, 300]), [0, 0, 0]).eval(),
+    )
+
+
+def test_mixed_dimensionality_set_subtensor():
+    x = Normal.dist(mu=0, size=(3, 2))
+    y = x[1].set(MvNormal.dist(mu=[1, 1], cov=np.eye(2)))
+    z = y[2].set(Normal.dist(mu=2, size=(2,)))
+
+    # Because `y` is multivariate the last dimension of `z` must be summed over
+    test_val = np.zeros((3, 2))
+    logp_eval = logp(z, test_val).eval()
+    assert logp_eval.shape == (3,)
+    np.testing.assert_allclose(
+        logp_eval,
+        logp(Normal.dist(mu=[[0, 0], [1, 1], [2, 2]]), test_val).sum(-1).eval(),
+    )
+
+
+def test_invalid_indexing_core_dims():
+    x = pt.empty((2, 2))
+    rv = MvNormal.dist(cov=np.eye(2))
+    vv = x.type()
+
+    match_msg = "Indexing along core dimensions of multivariate SetSubtensor not supported"
+
+    y = x[[0, 1], [1, 0]].set(rv)
+    with pytest.raises(NotImplementedError, match=match_msg):
+        logp(y, vv)
+
+    y = x[np.array([[False, True], [True, False]])].set(rv)
+    with pytest.raises(NotImplementedError, match=match_msg):
+        logp(y, vv)
+
+    # Univariate indexing above multivariate core dims also not supported
+    z = y[0].set(rv)[0, 1].set(Normal.dist())
+    with pytest.raises(NotImplementedError, match=match_msg):
+        logp(z, vv)
+
+
+def test_invalid_broadcasted_set_subtensor():
+    rv_bcast = Normal.dist(mu=0)
+    base = pt.empty((5,))
+
+    rv = base[:3].set(rv_bcast)
+    vv = rv.type()
+
+    # Broadcasting is known at write time, and PyMC does not attempt to make SetSubtensor measurable
+    with pytest.raises(NotImplementedError):
+        logp(rv, vv)
+
+    mask = pt.tensor(shape=(5,), dtype=bool)
+    rv = base[mask].set(rv_bcast)
+
+    # Broadcasting is only known at runtime, and PyMC raises an error when it happens
+    logp_rv = logp(rv, vv)
+    fn = pytensor.function([mask, vv], logp_rv)
+    test_vv = np.zeros(5)
+
+    np.testing.assert_allclose(
+        fn([False, False, True, False, False], test_vv),
+        [0, 0, -0.91893853, 0, 0],
+    )
+
+    with pytest.raises(
+        NotImplementedError,
+        match="Measurable SetSubtensor not supported when set value is broadcasted.",
+    ):
+        fn([False, False, True, False, True], test_vv)