diff --git a/CHANGELOG.md b/CHANGELOG.md
index c5cb848..16a3a2d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,15 @@
 
 ## Unreleased
 
+### Fixed
+
+- `is_identity()` implementation for Identity, Translate, Scale
+
+### Changed
+
+- `TransformSequence` can now be empty with `.empty(ndim)` constructor
+- `TransformGraph.get_sequence` can now handle identity transforms (i.e. space A to space A) [issues/86](https://github.com/clbarnes/transformnd/issues/86)
+
 ## 0.8.0 - 2026-08-28
 
 ### Added
diff --git a/justfile b/justfile
index c004cfb..172a718 100644
--- a/justfile
+++ b/justfile
@@ -36,9 +36,11 @@ format:
 test:
     uv run --all-groups --all-extras pytest -v
 
+# Run marimo server for editing examples.
 example-edit example:
     uv run --group examples marimo edit examples/{{example}}.py
 
+# Run marimo examples headless.
 example-test:
     uv run --group examples marimo export session examples --force-overwrite
 
@@ -46,6 +48,7 @@ example-test:
 bench:
     uv run --group test pytest --benchmark-only
 
+# Bump version, creating a git tag and changelog entry. Level can be "major", "minor", or "patch".
 bump level:
     test -z "$(git status --porcelain)" || ( git status && false )
     uv version --bump {{level}}
@@ -54,8 +57,10 @@ bump level:
     git commit -m "Bump to v$(uv version --short)"
     git tag -a "v$(uv version --short)" -m "$(changelog entry latest)"
 
+# Run pre-commit hooks on all files.
 pre-commit:
     uv run --group dev prek run --all-files
 
+# Run a REPL with all dependencies installed.
 repl:
     uv run --all-groups --all-extras --with ipython ipython
diff --git a/src/transformnd/base.py b/src/transformnd/base.py
index abb7841..22bb2c0 100644
--- a/src/transformnd/base.py
+++ b/src/transformnd/base.py
@@ -240,7 +240,11 @@ def as_transform_list(t: Transform[ArrayT]) -> list[Transform[ArrayT]]:
 
 
 class TransformSequence(Transform[ArrayT], Sequence[Transform[ArrayT]]):
-    """Chain transforms, applying one after another."""
+    """Chain transforms, applying one after another.
+
+    The `TransformSequence()` constructor takes a sequence of transforms which must not be empty.
+    Empty sequences can be handled with `TransformSequence.empty(ndim: int)`.
+    """
 
     def __init__(
         self,
@@ -248,8 +252,10 @@ def __init__(
     ) -> None:
         """Combine transforms by chaining them.
 
-        Also checks for consistent dimensionality and space references,
-        inferring if None.
+        Empty sequences raise an error;
+        use the `TransformSequence.empty(ndim)` constructor instead.
+
+        Also checks for consistent dimensionality.
 
         Parameters
         ----------
@@ -260,11 +266,13 @@ def __init__(
         Raises
         ------
         ValueError
-            If spaces are incompatible.
+            If spaces are incompatible, or no spaces are given.
         """
         ts = list(transforms)
         if not ts:
-            raise ValueError("Empty transform sequence")
+            raise ValueError(
+                "Empty transform sequence; use TransformSequence.empty(ndim)"
+            )
 
         for idx, (t1, t2) in enumerate(pairwise(ts)):
             if t1.ndims.target != t2.ndims.source:
@@ -280,6 +288,14 @@ def __init__(
 
         self.transforms: list[Transform[ArrayT]] = ts
 
+    @classmethod
+    def empty(cls, ndim: int) -> Self:
+        from .transforms import Identity
+
+        out = cls([Identity(ndim)])
+        out.transforms.pop()
+        return out
+
     def __iter__(self) -> Iterator[Transform[ArrayT]]:
         """Iterate through component transforms.
 
@@ -299,6 +315,9 @@ def __len__(self) -> int:
         return len(self.transforms)
 
     def invert(self) -> Transform[ArrayT] | None:
+        if self.is_empty():
+            return type(self).empty(self.ndims.source)
+
         try:
             transforms = [~t for t in reversed(self.transforms)]
         except NotImplementedError:
@@ -314,7 +333,8 @@ def apply(self, coords: ArrayT) -> ArrayT:
 
     def to_device(self, xp: ModuleType, device: str | None = None) -> Self:
         result = copy(self)
-        result.transforms = [t.to_device(xp, device) for t in self.transforms]
+        if not self.is_empty():
+            result.transforms = [t.to_device(xp, device) for t in self.transforms]
         return result
 
     def __str__(self) -> str:
@@ -329,10 +349,16 @@ def __getitem__(self, idx: slice | int):
     def is_identity(self) -> bool:
         return all(t.is_identity() for t in self)
 
+    def is_empty(self) -> bool:
+        return not self.transforms
+
     def flatten(self, drop_inverse: bool = True) -> Self:
         """Flatten nested sequences."""
         from .transforms.bijection import Bijection
 
+        if self.is_empty():
+            return copy(self)
+
         out: list[Transform[ArrayT]] = []
 
         for t in self.transforms:
@@ -357,7 +383,8 @@ def simplify(self, drop_inverse: bool = True):
         Does not check whether transforms invert each other,
         e.g. `Translation(1) | Translation(-1)`.
         """
-        from .transforms import Identity
+        if self.is_empty():
+            return copy(self)
 
         out: list[Transform[ArrayT]] = []
         affine = None
@@ -383,11 +410,13 @@ def simplify(self, drop_inverse: bool = True):
             add_to_output(affine, out)
 
         if not out:
-            out.append(Identity(self.ndims.source))
+            return type(self).empty(self.ndims.source)
 
         return type(self)(out)
 
     def to_affine(self) -> Affine[ArrayT] | None:
+        if self.is_empty():
+            return Affine.identity(self.ndims.source)  # type:ignore
         simple = self.simplify(True)
         if len(simple) != 1:
             return None
diff --git a/src/transformnd/graph.py b/src/transformnd/graph.py
index 78233e1..61c0c58 100644
--- a/src/transformnd/graph.py
+++ b/src/transformnd/graph.py
@@ -225,7 +225,21 @@ def get_sequence(
         -------
         TransformSequence[ArrayT]
             The shortest transform sequence between the spaces.
+
+        Raises
+        ------
+        ValueError
+            Unknown source or target space.
         """
+        src_ndim = self.ndim(source_space)
+        if src_ndim is None:
+            raise ValueError(f"Unknown source space {source_space}")
+        elif source_space == target_space:
+            return TransformSequence.empty(src_ndim)  # type:ignore
+
+        if self.ndim(target_space) is None:
+            raise ValueError(f"Unknown target space {source_space}")
+
         path = nx.shortest_path(self.graph, source_space, target_space, weight)  # type:ignore
         transforms = []
         if len(path) == 1:
diff --git a/src/transformnd/transforms/simple.py b/src/transformnd/transforms/simple.py
index 8c4678e..833768b 100644
--- a/src/transformnd/transforms/simple.py
+++ b/src/transformnd/transforms/simple.py
@@ -45,6 +45,9 @@ def apply(self, coords: ArrayT) -> ArrayT:
     def __str__(self) -> str:
         return f"{super().__str__()}({self.ndims.source})"
 
+    def is_identity(self) -> bool:
+        return True
+
 
 class Translate(Transform[ArrayT]):
     """Translate coordinates by addition."""
@@ -72,6 +75,10 @@ def __init__(
             )
         super().__init__(NDims(len(self.translation), len(self.translation)))
 
+    def is_identity(self) -> bool:
+        xp = array_namespace(self.translation)
+        return xp.all(self.translation == 0)
+
     def to_affine(self) -> Affine[ArrayT]:
         return Affine[ArrayT].translation(self.translation)
 
@@ -140,3 +147,7 @@ def to_device(self, xp: ModuleType, device: str | None = None) -> Self:
 
     def __str__(self) -> str:
         return f"{super().__str__()}({join_strs(self.scale)})"
+
+    def is_identity(self) -> bool:
+        xp = array_namespace(self.scale)
+        return xp.all(self.scale == 1)
diff --git a/tests/test_base.py b/tests/test_base.py
index f2eb170..7f2278f 100644
--- a/tests/test_base.py
+++ b/tests/test_base.py
@@ -121,3 +121,12 @@ def test_to_affine_no():
     seq = TransformSequence([t1, t2, t3])
     aff = seq.to_affine()
     assert aff is None
+
+
+def test_empty_seq():
+    t = TransformSequence.empty(2)
+    assert t.is_identity()
+    assert t.ndims.source == 2
+
+    with pytest.raises(ValueError):
+        t = TransformSequence([])
diff --git a/tests/test_graph.py b/tests/test_graph.py
index bf79708..083ce92 100644
--- a/tests/test_graph.py
+++ b/tests/test_graph.py
@@ -87,6 +87,13 @@ def test_multigraph():
     assert isinstance(seq[0], Translate)
 
 
+def test_identity_sequence():
+    g = TransformGraph()
+    g.add_transform(Spaced(Translate([1, 2, 3]), "a", "b"))
+    seq = g.get_sequence("a", "a")
+    assert seq.is_identity()
+
+
 if __name__ == "__main__":
     test_graph_traversal()
     print("All tests passed!")