diff --git a/ggml/src/ggml-cpu/ggml-cpu.cpp b/ggml/src/ggml-cpu/ggml-cpu.cpp
index 74631c285..16cc5116c 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.cpp
+++ b/ggml/src/ggml-cpu/ggml-cpu.cpp
@@ -469,6 +469,8 @@ static bool ggml_backend_cpu_device_supports_op(ggml_backend_dev_t dev, const st
             return (src0->type == GGML_TYPE_F32 ||
                     ((src0->type == GGML_TYPE_F16 || ggml_is_quantized(src0->type)) && src0->ne[2] == src1->ne[2] && src0->ne[3] == src1->ne[3])) &&
                 src1->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32;
+        case GGML_OP_CONV_2D:
+            return ggml_is_contiguous(op->src[0]);
         default:
             return true;
     }
diff --git a/ggml/src/ggml-cuda/conv2d.cu b/ggml/src/ggml-cuda/conv2d.cu
index 142dd6690..14774d4a5 100644
--- a/ggml/src/ggml-cuda/conv2d.cu
+++ b/ggml/src/ggml-cuda/conv2d.cu
@@ -126,6 +126,7 @@ void ggml_cuda_op_conv2d(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     const float *       X_D    = (const float *) input->data;
     float *             Y_D    = (float *) dst->data;
 
+    GGML_ASSERT(ggml_is_contiguous(input));
     GGML_ASSERT(ggml_is_contiguous(kernel));
     GGML_ASSERT(kernel->type == GGML_TYPE_F16 || kernel->type == GGML_TYPE_F32);
 
diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 3e2c62295..561ab7ac5 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -5105,7 +5105,7 @@ static bool ggml_backend_cuda_device_supports_op(ggml_backend_dev_t dev, const g
         case GGML_OP_IM2COL:
         case GGML_OP_IM2COL_3D:
         case GGML_OP_CONV_2D:
-            return true;
+            return (ggml_is_contiguous(op->src[0]) && ggml_is_contiguous(op->src[1]));
         case GGML_OP_CONV_2D_DW:
             return op->src[0]->type == GGML_TYPE_F32;
         case GGML_OP_CONV_TRANSPOSE_2D:
diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 49fd6e0b4..8a1bff65a 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -18016,10 +18016,17 @@ static bool ggml_backend_vk_device_supports_op(ggml_backend_dev_t dev, const ggm
         case GGML_OP_CONV_2D:
         case GGML_OP_CONV_TRANSPOSE_2D:
             {
+                const bool transpose = op->op == GGML_OP_CONV_TRANSPOSE_2D;
+                const int64_t cout = !transpose ? op->src[0]->ne[3] : op->src[0]->ne[2];
+                const int64_t cin  = !transpose ? op->src[0]->ne[2] : op->src[0]->ne[3];
+
                 // Channel-contiguous format is not supported yet.
                 return ((op->src[0]->type == GGML_TYPE_F32 || op->src[0]->type == GGML_TYPE_F16) &&
+                    (op->src[0]->nb[0] == sizeof(float) || op->src[0]->nb[0] == sizeof(ggml_fp16_t) ) &&
                     op->src[1]->type == GGML_TYPE_F32 &&
                     op->type == GGML_TYPE_F32 &&
+                    cout == op->ne[2] &&
+                    cin == op->src[1]->ne[2] &&
                     ggml_is_contiguous(op->src[0]) &&
                     ggml_is_contiguous(op->src[1]) &&
                     ggml_is_contiguous(op));