diff --git a/pymc/data.py b/pymc/data.py
index c21ac3001f..4b3538a340 100644
--- a/pymc/data.py
+++ b/pymc/data.py
@@ -30,13 +30,12 @@
 from pytensor.compile.sharedvalue import SharedVariable
 from pytensor.graph.basic import Variable
 from pytensor.raise_op import Assert
-from pytensor.scalar import Cast
-from pytensor.tensor.elemwise import Elemwise
 from pytensor.tensor.random.basic import IntegersRV
 from pytensor.tensor.variable import TensorConstant, TensorVariable
 
 import pymc as pm
 
+from pymc.logprob.utils import rvs_in_graph
 from pymc.pytensorf import convert_data
 from pymc.vartypes import isgenerator
 
@@ -111,13 +110,7 @@ def is_valid_observed(v) -> bool:
         return True
 
     return (
-        # The only PyTensor operation we allow on observed data is type casting
-        # Although we could allow for any graph that does not depend on other RVs
-        (
-            isinstance(v.owner.op, Elemwise)
-            and isinstance(v.owner.op.scalar_op, Cast)
-            and is_valid_observed(v.owner.inputs[0])
-        )
+        not rvs_in_graph(v)
         # Or Minibatch
         or (
             isinstance(v.owner.op, MinibatchOp)
@@ -148,7 +141,7 @@ def Minibatch(variable: TensorVariable, *variables: TensorVariable, batch_size:
     for i, v in enumerate(tensors):
         if not is_valid_observed(v):
             raise ValueError(
-                f"{i}: {v} is not valid for Minibatch, only constants or constants.astype(dtype) are allowed"
+                f"{i}: {v} is not valid for Minibatch, only non-random variables are allowed"
             )
 
     upper = tensors[0].shape[0]
diff --git a/pymc/pytensorf.py b/pymc/pytensorf.py
index cf5700b95e..82eca936b7 100644
--- a/pymc/pytensorf.py
+++ b/pymc/pytensorf.py
@@ -164,6 +164,12 @@ def extract_obs_data(x: TensorVariable) -> np.ndarray:
             mask[mask_idx] = 1
             return np.ma.MaskedArray(array_data, mask)
 
+    from pymc.logprob.utils import rvs_in_graph
+
+    if not inputvars(x) and not rvs_in_graph(x):
+        cheap_eval_mode = Mode(linker="py", optimizer=None)
+        return x.eval(mode=cheap_eval_mode)
+
     raise TypeError(f"Data cannot be extracted from {x}")
 
 
diff --git a/tests/test_data.py b/tests/test_data.py
index 154737b637..afca1831a7 100644
--- a/tests/test_data.py
+++ b/tests/test_data.py
@@ -509,11 +509,17 @@ def test_allowed(self):
         mb = pm.Minibatch(pt.as_tensor(self.data).astype(int), batch_size=20)
         assert isinstance(mb.owner.op, MinibatchOp)
 
-        with pytest.raises(ValueError, match="not valid for Minibatch"):
-            pm.Minibatch(pt.as_tensor(self.data) * 2, batch_size=20)
+        mb = pm.Minibatch(pt.as_tensor(self.data) * 2, batch_size=20)
+        assert isinstance(mb.owner.op, MinibatchOp)
+
+        for mb in pm.Minibatch(self.data, pt.as_tensor(self.data) * 2, batch_size=20):
+            assert isinstance(mb.owner.op, MinibatchOp)
 
-        with pytest.raises(ValueError, match="not valid for Minibatch"):
-            pm.Minibatch(self.data, pt.as_tensor(self.data) * 2, batch_size=20)
+    def test_not_allowed(self):
+        data = pt.random.normal(loc=self.data, scale=1)
+
+        with pytest.raises(ValueError):
+            pm.Minibatch(data, batch_size=20)
 
     def test_assert(self):
         d1, d2 = pm.Minibatch(self.data, self.data[::2], batch_size=20)
@@ -530,3 +536,21 @@ def test_multiple_vars(self):
         [draw_mA, draw_mB] = pm.draw([mA, mB])
         assert draw_mA.shape == (10,)
         np.testing.assert_allclose(draw_mA, -draw_mB)
+
+
+def test_scaling_data_works_in_likelihood() -> None:
+    data = np.array([10, 11, 12, 13, 14, 15])
+
+    with pm.Model():
+        target = pm.Data("target", data)
+        scale = 12
+        scaled_target = target / scale
+        mu = pm.Normal("mu", mu=0, sigma=1)
+        pm.Normal("x", mu=mu, sigma=1, observed=scaled_target)
+
+        idata = pm.sample(10, chains=1, tune=100)
+
+    np.testing.assert_allclose(
+        idata.observed_data["x"].values,
+        data / scale,
+    )
diff --git a/tests/test_pytensorf.py b/tests/test_pytensorf.py
index b8c82886b9..34360397a3 100644
--- a/tests/test_pytensorf.py
+++ b/tests/test_pytensorf.py
@@ -195,6 +195,21 @@ def test_minibatch_variable(self):
         assert isinstance(res, np.ndarray)
         np.testing.assert_array_equal(res, y)
 
+    def test_pytensor_operations(self):
+        x = np.array([1, 2, 3])
+        target = 1 + 3 * pt.as_tensor_variable(x)
+
+        res = extract_obs_data(target)
+        assert isinstance(res, np.ndarray)
+        np.testing.assert_array_equal(res, np.array([4, 7, 10]))
+
+    def test_pytensor_operations_raises(self):
+        x = pt.scalar("x")
+        target = 1 + 3 * x
+
+        with pytest.raises(TypeError, match="Data cannot be extracted from"):
+            extract_obs_data(target)
+
 
 @pytest.mark.parametrize("input_dtype", ["int32", "int64", "float32", "float64"])
 def test_convert_data(input_dtype):