diff --git a/python-package/xgboost/dask.py b/python-package/xgboost/dask.py
index 6286e2c21..b3a1f770a 100644
--- a/python-package/xgboost/dask.py
+++ b/python-package/xgboost/dask.py
@@ -326,10 +326,10 @@ class DaskDMatrix:
             self.partition_order[part.key] = i
 
         key_to_partition = {part.key: part for part in parts}
-        who_has = await client.scheduler.who_has(
-            keys=[part.key for part in parts])
+        who_has = await client.scheduler.who_has(keys=[part.key for part in parts])
 
         worker_map = defaultdict(list)
+
         for key, workers in who_has.items():
             worker_map[next(iter(workers))].append(key_to_partition[key])
 
@@ -651,9 +651,9 @@ async def _train_async(client, params, dtrain: DaskDMatrix, *args, evals=(),
             'The evaluation history is returned as result of training.')
 
     workers = list(_get_client_workers(client).keys())
-    rabit_args = await _get_rabit_args(workers, client)
+    _rabit_args = await _get_rabit_args(workers, client)
 
-    def dispatched_train(worker_addr, dtrain_ref, evals_ref):
+    def dispatched_train(worker_addr, rabit_args, dtrain_ref, evals_ref):
         '''Perform training on a single worker.  A local function prevents pickling.
 
         '''
@@ -699,8 +699,13 @@ async def _train_async(client, params, dtrain: DaskDMatrix, *args, evals=(),
     if evals:
         evals = [(e.create_fn_args(), name) for e, name in evals]
 
+    # Note for function purity:
+    # XGBoost is deterministic in most of the cases, which means train function is
+    # supposed to be idempotent.  One known exception is gblinear with shotgun updater.
+    # We haven't been able to do a full verification so here we keep pure to be False.
     futures = client.map(dispatched_train,
                          workers,
+                         [_rabit_args] * len(workers),
                          [dtrain.create_fn_args()] * len(workers),
                          [evals] * len(workers),
                          pure=False,
diff --git a/src/common/quantile.cu b/src/common/quantile.cu
index 29c71555c..6c5f162c3 100644
--- a/src/common/quantile.cu
+++ b/src/common/quantile.cu
@@ -369,6 +369,7 @@ size_t SketchContainer::ScanInput(Span<SketchEntry> entries, Span<OffsetT> d_col
    * from user input data.  Second is duplicated sketching entries, which is generated by
    * prunning or merging. We preserve the first type and remove the second type.
    */
+  timer_.Start(__func__);
   dh::safe_cuda(cudaSetDevice(device_));
   CHECK_EQ(d_columns_ptr_in.size(), num_columns_ + 1);
   dh::XGBCachingDeviceAllocator<char> alloc;
diff --git a/tests/python/test_with_dask.py b/tests/python/test_with_dask.py
index 6f12f93a2..8b4a56ac2 100644
--- a/tests/python/test_with_dask.py
+++ b/tests/python/test_with_dask.py
@@ -17,20 +17,23 @@ if sys.platform.startswith("win"):
 pytestmark = pytest.mark.skipif(**tm.no_dask())
 
 try:
-    from distributed import LocalCluster, Client
+    from distributed import LocalCluster, Client, get_client
     from distributed.utils_test import client, loop, cluster_fixture
     import dask.dataframe as dd
     import dask.array as da
     from xgboost.dask import DaskDMatrix
+    import dask
 except ImportError:
     LocalCluster = None
     Client = None
+    get_client = None
     client = None
     loop = None
     cluster_fixture = None
     dd = None
     da = None
     DaskDMatrix = None
+    dask = None
 
 kRows = 1000
 kCols = 10
@@ -142,7 +145,7 @@ def test_boost_from_prediction(tree_method):
     y_ = dd.from_array(y, chunksize=100)
 
     with LocalCluster(n_workers=4) as cluster:
-        with Client(cluster) as client:
+        with Client(cluster) as _:
             model_0 = xgb.dask.DaskXGBClassifier(
                 learning_rate=0.3,
                 random_state=123,
@@ -744,3 +747,39 @@ class TestDaskCallbacks:
         assert hasattr(booster, 'best_score')
         dump = booster.get_dump(dump_format='json')
         assert len(dump) - booster.best_iteration == early_stopping_rounds + 1
+
+    def test_data_initialization(self):
+        '''Assert each worker has the correct amount of data, and DMatrix initialization doesn't
+        generate unnecessary copies of data.
+
+        '''
+        with LocalCluster(n_workers=2) as cluster:
+            with Client(cluster) as client:
+                X, y = generate_array()
+                n_partitions = X.npartitions
+                m = xgb.dask.DaskDMatrix(client, X, y)
+                workers = list(xgb.dask._get_client_workers(client).keys())
+                rabit_args = client.sync(xgb.dask._get_rabit_args, workers, client)
+                n_workers = len(workers)
+
+                def worker_fn(worker_addr, data_ref):
+                    with xgb.dask.RabitContext(rabit_args):
+                        local_dtrain = xgb.dask._dmatrix_from_worker_map(**data_ref)
+                        assert local_dtrain.num_row() == kRows / n_workers
+
+                futures = client.map(
+                    worker_fn, workers, [m.create_fn_args()] * len(workers),
+                    pure=False, workers=workers)
+                client.gather(futures)
+
+                has_what = client.has_what()
+                cnt = 0
+                data = set()
+                for k, v in has_what.items():
+                    for d in v:
+                        cnt += 1
+                        data.add(d)
+
+                assert len(data) == cnt
+                # Subtract the on disk resource from each worker
+                assert cnt - n_workers == n_partitions