diff --git a/src/torchjd/autogram/_module_hook_manager.py b/src/torchjd/autogram/_module_hook_manager.py
index 273131d2..6e0f138b 100644
--- a/src/torchjd/autogram/_module_hook_manager.py
+++ b/src/torchjd/autogram/_module_hook_manager.py
@@ -9,7 +9,7 @@
 
 from ._edge_registry import EdgeRegistry
 from ._gramian_accumulator import GramianAccumulator
-from ._vjp import AutogradVJP, FunctionalVJP, VJPType
+from ._vjp import VJP, AutogradVJP, FunctionalVJP, Vmapped
 
 # Note about import from protected _pytree module:
 # PyTorch maintainers plan to make pytree public (see
@@ -93,7 +93,7 @@ class AccumulateJacobian(torch.autograd.Function):
     @staticmethod
     def forward(
         output_spec: TreeSpec,
-        vjp: VJPType,
+        vjp: VJP,
         args: PyTree,
         gramian_accumulator: GramianAccumulator,
         module: nn.Module,
@@ -110,7 +110,7 @@ def vmap(
         _,
         in_dims: PyTree,
         output_spec: TreeSpec,
-        vjp: VJPType,
+        vjp: VJP,
         args: PyTree,
         gramian_accumulator: GramianAccumulator,
         module: nn.Module,
@@ -157,7 +157,7 @@ class JacobianAccumulator(torch.autograd.Function):
     def forward(
         gramian_accumulation_phase: BoolRef,
         output_spec: TreeSpec,
-        vjp: VJPType,
+        vjp: VJP,
         args: PyTree,
         gramian_accumulator: GramianAccumulator,
         module: nn.Module,
@@ -166,7 +166,7 @@ def forward(
         return tuple(x.detach() for x in xs)
 
     # For Python version > 3.10, the type of `inputs` should become
-    # tuple[BoolRef, TreeSpec, VJPType, PyTree, GramianAccumulator, nn.Module, *tuple[Tensor, ...]]
+    # tuple[BoolRef, TreeSpec, VJP, PyTree, GramianAccumulator, nn.Module, *tuple[Tensor, ...]]
     @staticmethod
     def setup_context(
         ctx,
@@ -232,8 +232,9 @@ def __call__(self, module: nn.Module, args: PyTree, output: PyTree) -> PyTree:
         index = cast(int, preference.argmin().item())
         self.target_edges.register(get_gradient_edge(flat_outputs[index]))
 
+        vjp: VJP
         if self.has_batch_dim:
-            vjp = torch.vmap(FunctionalVJP(module))
+            vjp = Vmapped(FunctionalVJP(module))
         else:
             vjp = AutogradVJP(module, flat_outputs)
 
diff --git a/src/torchjd/autogram/_vjp.py b/src/torchjd/autogram/_vjp.py
index b05a7408..6520e969 100644
--- a/src/torchjd/autogram/_vjp.py
+++ b/src/torchjd/autogram/_vjp.py
@@ -15,11 +15,18 @@
 # still support older versions of PyTorch where pytree is protected).
 
 
-# This includes vmapped VJPs, which are not of type VJP.
-VJPType = Callable[[PyTree, PyTree], dict[str, Tensor]]
+class VJP(ABC):
+    """Represents an abstract VJP function."""
 
+    @abstractmethod
+    def __call__(self, grad_outputs: PyTree, inputs: PyTree) -> dict[str, Tensor]:
+        """
+        Computes and returns the dictionary of parameter names to their gradients for the given
+        grad_outputs (cotangents) and at the given inputs.
+        """
 
-class VJP(ABC):
+
+class ModuleVJP(VJP, ABC):
     """
     Represents an abstract VJP function for a module's forward pass with respect to its parameters.
 
@@ -37,15 +44,19 @@ def __init__(self, module: nn.Module):
             else:
                 self.frozen_params[name] = param
 
-    @abstractmethod
+
+class Vmapped(VJP):
+    """VJP wrapper that applies the wrapped VJP, vmapped on the first dimension."""
+
+    def __init__(self, vjp: VJP):
+        super().__init__()
+        self.vmapped_vjp = torch.vmap(vjp)
+
     def __call__(self, grad_outputs: PyTree, inputs: PyTree) -> dict[str, Tensor]:
-        """
-        Computes and returns the dictionary of parameter names to their gradients for the given
-        grad_outputs (cotangents) and at the given inputs.
-        """
+        return self.vmapped_vjp(grad_outputs, inputs)
 
 
-class FunctionalVJP(VJP):
+class FunctionalVJP(ModuleVJP):
     """
     Represents a VJP function for a module's forward pass with respect to its parameters using the
     func api. The __call__ function takes both the inputs and the cotangents that can be vmapped
@@ -95,7 +106,7 @@ def functional_model_call(primals: dict[str, Parameter]) -> Tensor:
         return torch.func.vjp(functional_model_call, self.trainable_params)[1]
 
 
-class AutogradVJP(VJP):
+class AutogradVJP(ModuleVJP):
     """
     Represents a VJP function for a module's forward pass with respect to its parameters using the
     autograd engine. The __call__ function takes both the inputs and the cotangents but ignores the