diff --git a/doc/changes/DM-50244.misc.md b/doc/changes/DM-50244.misc.md
new file mode 100644
index 000000000..e667865d6
--- /dev/null
+++ b/doc/changes/DM-50244.misc.md
@@ -0,0 +1 @@
+Make quantum graph generation more permissive about missing init-outputs in `--skip-existing-in` collections.
diff --git a/python/lsst/pipe/base/quantum_graph_builder.py b/python/lsst/pipe/base/quantum_graph_builder.py
index 072b9b813..786a87545 100644
--- a/python/lsst/pipe/base/quantum_graph_builder.py
+++ b/python/lsst/pipe/base/quantum_graph_builder.py
@@ -346,8 +346,16 @@ def build(
             # Loop over tasks.  The pipeline graph must be topologically
             # sorted, so a quantum is only processed after any quantum that
             # provides its inputs has been processed.
+            doomed_tasks: list[str] = []
             for task_node in self._pipeline_graph.tasks.values():
-                self._resolve_task_quanta(task_node, full_skeleton)
+                doomed_tasks.extend(self._resolve_task_quanta(task_node, full_skeleton))
+            for task_label in doomed_tasks:
+                if full_skeleton.has_task(task_label):
+                    raise InitInputMissingError(
+                        f"Task {task_label} requires an init-output dataset that was not present "
+                        f"in {self.skip_existing_in} and cannot be produced by this graph. "
+                        "(see warnings logged earlier for details)."
+                    )
             # Add global init-outputs to the skeleton.
             for dataset_type in self._global_init_output_types.values():
                 dataset_key = full_skeleton.add_dataset_node(
@@ -427,7 +435,7 @@ class can add them later, albeit possibly less efficiently).
 
     @final
     @timeMethod
-    def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkeleton) -> None:
+    def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkeleton) -> list[str]:
         """Process the quanta for one task in a skeleton graph to skip those
         that have already completed and adjust those that request it.
 
@@ -438,6 +446,14 @@ def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkelet
         skeleton : `quantum_graph_skeleton.QuantumGraphSkeleton`
             Preliminary quantum graph, to be modified in-place.
 
+        Returns
+        -------
+        doomed_tasks : `list` [ `str` ]
+            Labels of tasks that consume an init-output that will not be
+            produced by this quantum graph, because the producing task is being
+            dropped due to skip-existing-in and the output was not present in
+            the skip-existing-in collection.
+
         Notes
         -----
         This method modifies ``skeleton`` in-place in several ways:
@@ -507,6 +523,7 @@ def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkelet
             # raise if one of the check conditions is not met, which is the
             # intended behavior.
             helper = AdjustQuantumHelper(inputs=adjusted_inputs, outputs=adjusted_outputs)
+            quantum_data_id = skeleton[quantum_key]["data_id"]
             try:
                 helper.adjust_in_place(task_node.get_connections(), task_node.label, quantum_data_id)
             except NoWorkFound as err:
@@ -561,7 +578,7 @@ def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkelet
         for no_work_quantum in no_work_quanta:
             skeleton.remove_quantum_node(no_work_quantum, remove_outputs=True)
         remaining_quanta = skeleton.get_quanta(task_node.label)
-        self._resolve_task_init(task_node, skeleton, bool(skipped_quanta))
+        doomed_tasks = self._resolve_task_init(task_node, skeleton, bool(skipped_quanta))
         message_terms = []
         if no_work_quanta:
             message_terms.append(f"{len(no_work_quanta)} had no work to do")
@@ -582,6 +599,7 @@ def _resolve_task_quanta(self, task_node: TaskNode, skeleton: QuantumGraphSkelet
                 "Dropping task %s because no quanta remain%s.", task_node.label, message_parenthetical
             )
             skeleton.remove_task(task_node.label)
+        return doomed_tasks
 
     def _skip_quantum_if_metadata_exists(
         self, task_node: TaskNode, quantum_key: QuantumKey, skeleton: QuantumGraphSkeleton
@@ -837,7 +855,7 @@ class and components defined by the task's own connections.
     @final
     def _resolve_task_init(
         self, task_node: TaskNode, skeleton: QuantumGraphSkeleton, has_skipped_quanta: bool
-    ) -> None:
+    ) -> list[str]:
         """Add init-input and init-output dataset nodes and edges for a task to
         the skeleton.
 
@@ -850,9 +868,18 @@ def _resolve_task_init(
         has_skipped_quanta : `bool`
             Whether any of this task's quanta were skipped because they had
             already succeeded.
+
+        Returns
+        -------
+        doomed_tasks : `list` [ `str` ]
+            Labels of tasks that consume an init-output that will not be
+            produced by this quantum graph, because the producing task is being
+            dropped due to skip-existing-in and the output was not present in
+            the skip-existing-in collection.
         """
         quanta = skeleton.get_quanta(task_node.label)
         task_init_key = TaskInitKey(task_node.label)
+        doomed_tasks: list[str] = []
         if quanta:
             adapted_inputs: NamedKeyDict[DatasetType, DatasetRef] = NamedKeyDict()
             # Process init-inputs.
@@ -910,11 +937,23 @@ def _resolve_task_init(
                     write_edge.parent_dataset_type_name, self.empty_data_id
                 )
                 if (ref := self.empty_dimensions_datasets.outputs_for_skip.get(dataset_key)) is None:
-                    raise InitInputMissingError(
-                        f"Init-output dataset {write_edge.parent_dataset_type_name!r} of skipped task "
-                        f"{task_node.label!r} not found in skip-existing-in collection(s) "
-                        f"{self.skip_existing_in}."
-                    ) from None
+                    # init-outputs really shouldn't be missing, but because
+                    # they might in important contexts (rapid analysis) we want
+                    # to try really hard to just warn and proceed without them.
+                    # First we see if any tasks are going to need those as
+                    # inputs, and later once we've dropped all the task we're
+                    # going to, we'll see if any remain that can't proceed.
+                    consuming_tasks = self._pipeline_graph.consumers_of(write_edge.parent_dataset_type_name)
+                    doomed_tasks.extend([n.label for n in consuming_tasks])
+                    self.log.warning(
+                        "Init-output dataset %r of skipped task %r not found in skip-existing-in "
+                        "collection(s) %s. Proceeding unless this is needed as an input by a retained task.",
+                        write_edge.parent_dataset_type_name,
+                        task_node.label,
+                        self.skip_existing_in,
+                    )
+                    skeleton.remove_dataset_nodes([dataset_key])
+                    continue
                 skeleton.set_dataset_ref(ref, dataset_key)
                 # If this dataset was "in the way" (i.e. already in the output
                 # run), it isn't anymore.
@@ -924,6 +963,7 @@ def _resolve_task_init(
         # dooms all downstream quanta to the same fate, so we don't bother
         # doing anything with the task's init-outputs, since nothing is
         # going to consume them.
+        return doomed_tasks
 
     @final
     @timeMethod