diff --git a/tests/BenchmarkDotNet.IntegrationTests/MemoryDiagnoserTests.cs b/tests/BenchmarkDotNet.IntegrationTests.ManualRunning/MemoryDiagnoserTests.cs
old mode 100755
new mode 100644
similarity index 94%
rename from tests/BenchmarkDotNet.IntegrationTests/MemoryDiagnoserTests.cs
rename to tests/BenchmarkDotNet.IntegrationTests.ManualRunning/MemoryDiagnoserTests.cs
index cf573f9985..fbe989fa88
--- a/tests/BenchmarkDotNet.IntegrationTests/MemoryDiagnoserTests.cs
+++ b/tests/BenchmarkDotNet.IntegrationTests.ManualRunning/MemoryDiagnoserTests.cs
@@ -24,8 +24,11 @@
 using Xunit.Abstractions;
 using BenchmarkDotNet.Toolchains.Mono;
 
-namespace BenchmarkDotNet.IntegrationTests
+namespace BenchmarkDotNet.IntegrationTests.ManualRunning
 {
+    // #1925
+    // These tests were moved to ManualRunning to stabilize the CI.
+    // Even after disabling tiered jit and blocking the finalizer thread, the tests are still flaky on CI.
     public class MemoryDiagnoserTests
     {
         private readonly ITestOutputHelper output;
@@ -51,7 +54,6 @@ public class AccurateAllocations
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void MemoryDiagnoserIsAccurate(IToolchain toolchain)
         {
             long objectAllocationOverhead = IntPtr.Size * 2; // pointer to method table + object header word
@@ -109,7 +111,6 @@ private void AllocateUntilGcWakesUp()
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void MemoryDiagnoserDoesNotIncludeAllocationsFromSetupAndCleanup(IToolchain toolchain)
         {
             AssertAllocations(toolchain, typeof(AllocatingGlobalSetupAndCleanup), new Dictionary<string, long>
@@ -135,7 +136,6 @@ public ulong TimeConsuming()
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void EngineShouldNotInterfereAllocationResults(IToolchain toolchain)
         {
             AssertAllocations(toolchain, typeof(NoAllocationsAtAll), new Dictionary<string, long>
@@ -146,7 +146,6 @@ public void EngineShouldNotInterfereAllocationResults(IToolchain toolchain)
 
         // #1542
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void TieredJitShouldNotInterfereAllocationResults(IToolchain toolchain)
         {
             AssertAllocations(toolchain, typeof(NoAllocationsAtAll), new Dictionary<string, long>
@@ -162,7 +161,6 @@ public class NoBoxing
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void EngineShouldNotIntroduceBoxing(IToolchain toolchain)
         {
             AssertAllocations(toolchain, typeof(NoBoxing), new Dictionary<string, long>
@@ -183,7 +181,6 @@ public class NonAllocatingAsynchronousBenchmarks
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void AwaitingTasksShouldNotInterfereAllocationResults(IToolchain toolchain)
         {
             AssertAllocations(toolchain, typeof(NonAllocatingAsynchronousBenchmarks), new Dictionary<string, long>
@@ -208,7 +205,6 @@ public void WithOperationsPerInvoke()
         }
 
         [Theory, MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void AllocatedMemoryShouldBeScaledForOperationsPerInvoke(IToolchain toolchain)
         {
             long objectAllocationOverhead = IntPtr.Size * 2; // pointer to method table + object header word
@@ -234,7 +230,6 @@ public byte[] SixtyFourBytesArray()
         }
 
         [TheoryEnvSpecific("Full Framework cannot measure precisely enough for low invocation counts.", EnvRequirement.DotNetCoreOnly), MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void AllocationQuantumIsNotAnIssueForNetCore21Plus(IToolchain toolchain)
         {
             long objectAllocationOverhead = IntPtr.Size * 2; // pointer to method table + object header word
@@ -300,7 +295,6 @@ public void Allocate()
 
         [TheoryEnvSpecific("Full Framework cannot measure precisely enough", EnvRequirement.DotNetCoreOnly)]
         [MemberData(nameof(GetToolchains))]
-        [Trait(Constants.Category, Constants.BackwardCompatibilityCategory)]
         public void MemoryDiagnoserIsAccurateForMultiThreadedBenchmarks(IToolchain toolchain)
         {
             long objectAllocationOverhead = IntPtr.Size * 2; // pointer to method table + object header word
@@ -325,12 +319,8 @@ private void AssertAllocations(IToolchain toolchain, Type benchmarkType, Diction
             }
             catch (MisconfiguredEnvironmentException e)
             {
-                if (ContinuousIntegration.IsLocalRun())
-                {
-                    output.WriteLine(e.SkipMessage);
-                    return;
-                }
-                throw;
+                output.WriteLine(e.SkipMessage);
+                return;
             }
 
             foreach (var benchmarkAllocationsValidator in benchmarksAllocationsValidators)