diff --git a/tlm_adjoint/torch.py b/tlm_adjoint/torch.py
index 7ba77139..6be0cd6c 100644
--- a/tlm_adjoint/torch.py
+++ b/tlm_adjoint/torch.py
@@ -30,11 +30,14 @@
     ]
 
 
-def to_torch_tensor(x, *args, **kwargs):
-    return torch.tensor(var_get_values(x), *args, **kwargs)
+def to_torch_tensor(x, *args, conjugate=False, **kwargs):
+    x_a = var_get_values(x)
+    if conjugate:
+        x_a = x_a.conjugate()
+    return torch.tensor(x_a, *args, **kwargs)
 
 
-def to_torch_tensors(X, *args, **kwargs):
+def to_torch_tensors(X, *args, conjugate=False, **kwargs):
     """Convert one or more variables to :class:`torch.Tensor` objects.
 
     Parameters
@@ -42,6 +45,8 @@ def to_torch_tensors(X, *args, **kwargs):
 
     X : variable or Sequence[variable, ...]
         Variables to be converted.
+    conjugate : bool
+        Whether to copy the complex conjugate.
     args, kwargs
         Passed to :func:`torch.tensor`.
 
@@ -52,15 +57,19 @@ def to_torch_tensors(X, *args, **kwargs):
         The converted variables.
     """
 
-    return tuple(to_torch_tensor(x, *args, **kwargs) for x in packed(X))
+    return tuple(to_torch_tensor(x, *args, conjugate=conjugate, **kwargs)
+                 for x in packed(X))
 
 
-def from_torch_tensor(x, x_t):
-    var_set_values(x, x_t.detach().numpy())
+def from_torch_tensor(x, x_t, *, conjugate=False):
+    x_a = x_t.detach().numpy()
+    if conjugate:
+        x_a = x_a.conjugate()
+    var_set_values(x, x_a)
     return x
 
 
-def from_torch_tensors(X, X_t):
+def from_torch_tensors(X, X_t, *, conjugate=False):
     """Copy data from PyTorch tensors into variables.
 
     Parameters
@@ -70,13 +79,15 @@ def from_torch_tensors(X, X_t):
         Output.
     X_t : Sequence[:class:`torch.Tensor`, ...]
         Input.
+    conjugate : bool
+        Whether to copy the complex conjugate.
     """
 
     X = packed(X)
     if len(X) != len(X_t):
         raise ValueError("Invalid length")
     for x, x_t in zip(X, X_t):
-        from_torch_tensor(x, x_t)
+        from_torch_tensor(x, x_t, conjugate=conjugate)
 
 
 @restore_manager
@@ -123,11 +134,12 @@ def backward(ctx, *adj_X_t):
                                    clear_caches=clear_caches)
             J_id[0] = var_id(J)
 
-        from_torch_tensors(adj_X, adj_X_t)
+        from_torch_tensors(adj_X, adj_X_t, conjugate=True)
         set_manager(manager)
         dJ = compute_gradient(J, M)
 
-        return (None, None, None, None, None) + to_torch_tensors(dJ)
+        return ((None, None, None, None, None)
+                + to_torch_tensors(dJ, conjugate=True))
 
 
 def torch_wrapped(forward, space, *, manager=None, clear_caches=True):