diff --git a/modules/dnn/src/net_impl.cpp b/modules/dnn/src/net_impl.cpp
index dc2444e994..ba9d6bc36b 100644
--- a/modules/dnn/src/net_impl.cpp
+++ b/modules/dnn/src/net_impl.cpp
@@ -1631,21 +1631,20 @@ void Net::Impl::setInput(InputArray blob, const String& name, double scalefactor
 
 Mat Net::Impl::getParam(int layer, int numParam) const
 {
-    LayerData& ld = getLayerData(layer);
-    std::vector<Mat>& layerBlobs = getLayerInstance(ld)->blobs;
+    std::vector<Mat>& layerBlobs = getLayer(layer)->blobs;
     CV_Assert(numParam < (int)layerBlobs.size());
     return layerBlobs[numParam];
 }
 
 void Net::Impl::setParam(int layer, int numParam, const Mat& blob)
 {
-    LayerData& ld = getLayerData(layer);
-
     // FIXIT we should not modify "execution" instance
-    std::vector<Mat>& layerBlobs = getLayerInstance(ld)->blobs;
+    std::vector<Mat>& layerBlobs = getLayer(layer)->blobs;
     CV_Assert(numParam < (int)layerBlobs.size());
     // we don't make strong checks, use this function carefully
     layerBlobs[numParam] = blob;
+    if (mainGraph)
+        finalizeLayers = true;
 }
 
 void Net::Impl::setParam(const std::string& outputTensorName, int numParam, const Mat& blob)
@@ -1657,9 +1656,16 @@ void Net::Impl::setParam(const std::string& outputTensorName, int numParam, cons
             if (excl != std::string::npos)
                 it = argnames.find(outputTensorName.substr(excl + 1));
         }
-        if (it == argnames.end())
+        if (it == argnames.end()) {
+            // Not a tensor name; try it as a layer name.
+            int lid = getLayerId(outputTensorName);
+            if (lid >= 0) {
+                setParam(lid, numParam, blob);
+                return;
+            }
             CV_Error_(Error::StsObjectNotFound,
                       ("DNN: tensor '%s' not found in the graph", outputTensorName.c_str()));
+        }
 
         int targetIdx = (int)it->second;
         const std::vector<Ptr<Layer>>& prog = mainGraph->prog();
diff --git a/modules/dnn/src/net_impl2.cpp b/modules/dnn/src/net_impl2.cpp
index 6fbabd8da6..e32f82e9b1 100644
--- a/modules/dnn/src/net_impl2.cpp
+++ b/modules/dnn/src/net_impl2.cpp
@@ -689,6 +689,24 @@ void Net::Impl::forwardMainGraph(InputArrayOfArrays inputs, OutputArrayOfArrays
         kvCacheManager.applyRoutes();
 }
 
+// Assign a single result to an output array, including a (pre-allocated) vector
+// of Mat/UMat, which _OutputArray::assign(Mat) does not handle.
+static void assignSingleOutput(OutputArrayOfArrays outputBlobs, const Mat& result)
+{
+    _InputArray::KindFlag k = outputBlobs.kind();
+    if (k == _InputArray::STD_VECTOR_MAT) {
+        std::vector<Mat>& v = outputBlobs.getMatVecRef();
+        v.resize(1);
+        result.copyTo(v[0]);
+    } else if (k == _InputArray::STD_VECTOR_UMAT) {
+        std::vector<UMat>& v = outputBlobs.getUMatVecRef();
+        v.resize(1);
+        result.copyTo(v[0]);
+    } else {
+        outputBlobs.assign(result);
+    }
+}
+
 void Net::Impl::forwardWithSingleOutput(const std::string& outname, OutputArrayOfArrays outputBlobs)
 {
 #ifdef HAVE_ONNXRUNTIME
@@ -715,7 +733,7 @@ void Net::Impl::forwardWithSingleOutput(const std::string& outname, OutputArrayO
         std::vector<int> outIdxs(1, outIdx);
         std::vector<Mat> outs = runOrtSession(netInputLayer->blobs, outIdxs);
         CV_Assert(outs.size() == 1);
-        outputBlobs.assign(outs[0]);
+        assignSingleOutput(outputBlobs, outs[0]);
         return;
     }
 #endif
@@ -743,7 +761,7 @@ void Net::Impl::forwardWithSingleOutput(const std::string& outname, OutputArrayO
             const std::vector<Arg>& gr_outputs = mainGraph->outputs();
             for (size_t i = 0; i < gr_outputs.size(); i++) {
                 if (gr_outputs[i].idx == targetArg.idx) {
-                    outputBlobs.assign(outs[i]);
+                    assignSingleOutput(outputBlobs, outs[i]);
                     return;
                 }
             }
@@ -760,9 +778,9 @@ void Net::Impl::forwardWithSingleOutput(const std::string& outname, OutputArrayO
             if (result.shape().layout == DATA_LAYOUT_BLOCK) {
                 Mat converted;
                 transformLayout(result, converted, originalLayout, originalLayout, defaultC0);
-                outputBlobs.assign(converted);
+                assignSingleOutput(outputBlobs, converted);
             } else {
-                outputBlobs.assign(result.clone());
+                assignSingleOutput(outputBlobs, result.clone());
             }
             return;
         }
@@ -771,7 +789,7 @@ void Net::Impl::forwardWithSingleOutput(const std::string& outname, OutputArrayO
     std::vector<Mat> inps, outs;
     forwardMainGraph(inps, outs);
     CV_Assert(!outs.empty());
-    outputBlobs.assign(outs[0]);
+    assignSingleOutput(outputBlobs, outs[0]);
 }
 
 void Net::Impl::forwardWithMultipleOutputs(OutputArrayOfArrays outblobs, const std::vector<std::string>& outnames)