diff --git a/lib/livebook/runtime/evaluator/io_proxy.ex b/lib/livebook/runtime/evaluator/io_proxy.ex
index e5ed12865..d3b85e8e5 100644
--- a/lib/livebook/runtime/evaluator/io_proxy.ex
+++ b/lib/livebook/runtime/evaluator/io_proxy.ex
@@ -262,6 +262,7 @@ defmodule Livebook.Runtime.Evaluator.IOProxy do
     {:ok, state}
   end
 
+  # This request is used by Kino <= 0.13.1
   defp io_request({:livebook_get_input_value, input_id}, state) do
     input_cache =
       Map.put_new_lazy(state.input_cache, input_id, fn ->
@@ -271,6 +272,25 @@ defmodule Livebook.Runtime.Evaluator.IOProxy do
     {input_cache[input_id], %{state | input_cache: input_cache}}
   end
 
+  defp io_request({:livebook_get_input_value, input_id, pid}, state) do
+    # We only allow reading the input value from the evaluator process,
+    # to make sure the cell is still evaluating. A different process
+    # could attempt to read the value after the cell evaluation was
+    # finished, in which case we could return a cached value from a
+    # different evaluation and we would not track the read properly.
+
+    if pid == state.evaluator do
+      input_cache =
+        Map.put_new_lazy(state.input_cache, input_id, fn ->
+          request_input_value(input_id, state)
+        end)
+
+      {input_cache[input_id], %{state | input_cache: input_cache}}
+    else
+      {{:error, :bad_process}, state}
+    end
+  end
+
   defp io_request({:livebook_get_file_path, file_id}, state) do
     # We could cache forever, but we don't want the cache to pile up
     # indefinitely, so we just reuse the input cache which is cleared
diff --git a/test/livebook/runtime/evaluator/io_proxy_test.exs b/test/livebook/runtime/evaluator/io_proxy_test.exs
index 16b3e8e2d..acc5eef52 100644
--- a/test/livebook/runtime/evaluator/io_proxy_test.exs
+++ b/test/livebook/runtime/evaluator/io_proxy_test.exs
@@ -18,7 +18,7 @@ defmodule Livebook.Runtime.Evaluator.IOProxyTest do
 
     io = Process.info(evaluator.pid)[:group_leader]
     IOProxy.before_evaluation(io, :ref, "cell")
-    %{io: io}
+    %{io: io, evaluator: evaluator}
   end
 
   describe ":stdio interoperability" do
@@ -47,7 +47,19 @@ defmodule Livebook.Runtime.Evaluator.IOProxyTest do
   end
 
   describe "input" do
-    test "responds to Livebook input request", %{io: io} do
+    test "responds to Livebook input request", %{io: io, evaluator: evaluator} do
+      pid =
+        spawn(fn ->
+          pid = evaluator.pid
+          assert livebook_get_input_value(io, "input1", pid) == {:ok, :value}
+        end)
+
+      reply_to_input_request(:ref, "input1", {:ok, :value}, 1)
+
+      await_termination(pid)
+    end
+
+    test "responds to Livebook input request (legacy)", %{io: io} do
       pid =
         spawn(fn ->
           assert livebook_get_input_value(io, "input1") == {:ok, :value}
@@ -58,11 +70,12 @@ defmodule Livebook.Runtime.Evaluator.IOProxyTest do
       await_termination(pid)
     end
 
-    test "responds to subsequent requests with the same value", %{io: io} do
+    test "responds to subsequent requests with the same value", %{io: io, evaluator: evaluator} do
       pid =
         spawn(fn ->
-          assert livebook_get_input_value(io, "input1") == {:ok, :value}
-          assert livebook_get_input_value(io, "input1") == {:ok, :value}
+          pid = evaluator.pid
+          assert livebook_get_input_value(io, "input1", pid) == {:ok, :value}
+          assert livebook_get_input_value(io, "input1", pid) == {:ok, :value}
         end)
 
       reply_to_input_request(:ref, "input1", {:ok, :value}, 1)
@@ -70,13 +83,25 @@ defmodule Livebook.Runtime.Evaluator.IOProxyTest do
       await_termination(pid)
     end
 
-    test "before_evaluation/3 clears all cached input information", %{io: io} do
+    test "responds with error, when request does not come from the evaluator process", %{io: io} do
+      pid =
+        spawn(fn ->
+          pid = self()
+          assert livebook_get_input_value(io, "input1", pid) == {:error, :bad_process}
+        end)
+
+      await_termination(pid)
+    end
+
+    test "before_evaluation/3 clears all cached input information",
+         %{io: io, evaluator: evaluator} do
       pid =
         spawn_link(fn ->
+          pid = evaluator.pid
           IOProxy.before_evaluation(io, :ref, "cell")
-          assert livebook_get_input_value(io, "input1") == {:ok, :value1}
+          assert livebook_get_input_value(io, "input1", pid) == {:ok, :value1}
           IOProxy.before_evaluation(io, :ref, "cell")
-          assert livebook_get_input_value(io, "input1") == {:ok, :value2}
+          assert livebook_get_input_value(io, "input1", pid) == {:ok, :value2}
         end)
 
       reply_to_input_request(:ref, "input1", {:ok, :value1}, 1)
@@ -177,6 +202,10 @@ defmodule Livebook.Runtime.Evaluator.IOProxyTest do
     io_request(io, {:livebook_get_input_value, input_id})
   end
 
+  defp livebook_get_input_value(io, input_id, pid) do
+    io_request(io, {:livebook_get_input_value, input_id, pid})
+  end
+
   defp livebook_generate_token(io) do
     io_request(io, :livebook_generate_token)
   end